The concentration-compactness principle in the calculus of variations. The limit case. I

DOI10.4171/RMI/6zbMath0704.49005OpenAlexW4244689643MaRDI QIDQ917005

Publication date: 1985

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/39314

zbMATH Keywords

functional inequalities Sobolev inequalities concentration-compactness principle

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence theories for free problems in two or more independent variables (49J10) Existence theories for problems in abstract spaces (49J27)

Related Items

Extremal function for Moser-Trudinger type inequality with logarithmic weight ⋮ On existence of extremizers for the Tomas-Stein inequality for $S^{1}$ ⋮ A weak compactness result for critical elliptic systems of $n$-harmonic type ⋮ Nonlocal problems at nearly critical growth ⋮ Sobolev inequalities for the Hardy-Schrödinger operator: extremals and critical dimensions ⋮ Entire solutions for a class of fourth-order semilinear elliptic equations with weights ⋮ A gamma convergence approach to the critical Sobolev embedding in variable exponent spaces ⋮ Multiple positive solutions for a Kirchhoff type problem with a critical nonlinearity ⋮ New results concerning Moser-type inequalities in Lorentz-Sobolev spaces ⋮ Optimal decay of extremals for the fractional Sobolev inequality ⋮ On a variational problem involving critical Sobolev growth in dimension three ⋮ A class of elliptic equations with singular and critical nonlinearities ⋮ Weighted fractional Sobolev inequality in $\mathbb R^N$ ⋮ Ground state solution for a Kirchhoff problem with exponential critical growth ⋮ On the best constants in Sobolev inequalities on the solid torus in the limit case $p = 1$ ⋮ Ground states for fractional Schrödinger equations involving a critical nonlinearity ⋮ On symmetric solutions of a critical semilinear elliptic system involving the Caffarelli-Kohn-Nirenberg inequality in $\mathbb{R}^{N}$ ⋮ Multiplicity results for the Kirchhoff type equations with critical growth ⋮ Polyharmonic Kirchhoff type equations with singular exponential nonlinearities ⋮ Concentrating bounded states for a class of singularly perturbed Kirchhoff type equations with a general nonlinearity ⋮ Solutions of the quasilinear elliptic systems with combined critical Sobolev-Hardy terms ⋮ Existence and multiplicity of positive solutions for a class of elliptic equations involving critical Sobolev exponents ⋮ Moser functions and fractional Moser-Trudinger type inequalities ⋮ Global dynamics above the ground state for the energy-critical Schrödinger equation with radial data ⋮ Concentrating solitary waves for a class of singularly perturbed quasilinear Schrödinger equations with a general nonlinearity ⋮ On the behavior of solutions of nonlinear Schrödinger equation with exponential growth ⋮ Sharp higher-order Sobolev inequalities in the hyperbolic space $\mathbb H^n$ ⋮ Curvature and bubble convergence of harmonic maps ⋮ Lie point symmetries of the Lane-Emden systems ⋮ On interpolation of cocompact imbeddings ⋮ On the compensated compactness principle ⋮ Optimal Sobolev type inequalities in Lorentz spaces ⋮ Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $\mathbb R^n$ ⋮ On the singular elliptic systems involving multiple critical Sobolev exponents ⋮ Multiple positive solutions for $p$-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term ⋮ A note on nonlinear fourth-order elliptic equations on $\mathbb R ^N$ ⋮ On the lack of compactness in the 2D critical Sobolev embedding ⋮ Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds ⋮ On the stability in weak topology of the set of global solutions to the Navier-Stokes equations ⋮ Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases ⋮ Systems of elliptic equations involving multiple critical nonlinearities and different Hardy-type terms in $\mathbb R^N$ ⋮ Elliptic systems involving critical nonlinearities and different Hardy-type terms ⋮ On a singular class of elliptic systems involving critical growth in $\mathbb R^2$ ⋮ On $G$-symmetric solutions of critical elliptic equations of Caffarelli-Kohn-Nirenberg type ⋮ An elliptic problem with an indefinite nonlinearity and a parameter in the boundary condition ⋮ Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in $\mathbb{R}^N$ ⋮ Concentration-compactness principle for an inequality by D.~ Adams ⋮ Existence and multiplicity results for quasilinear elliptic exterior problems with nonlinear boundary conditions ⋮ Origin and evolution of the Palais-Smale condition in critical point theory ⋮ Multiplicity of positive solutions for weighted quasilinear elliptic equations involving critical Hardy-Sobolev exponents and concave-convex nonlinearities ⋮ On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold ⋮ Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group ⋮ Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities ⋮ Beyond the Trudinger-Moser supremum ⋮ The asymptotic behavior of the ground state solutions for biharmonic equations ⋮ Semilinear systems involving multiple critical Hardy-Sobolev exponents and three singular points ⋮ Existence of positive solutions for a class of $p\&q$ elliptic problems with critical growth on $\mathbb R^N$ ⋮ Existence and multiplicity of symmetric solutions for semilinear elliptic equations with singular potentials and critical Hardy-Sobolev exponents ⋮ Existence of entire positive solutions for a critical system of nonlinear elliptic equations ⋮ Extremals for Sobolev and Moser inequalities in hyperbolic space ⋮ Subcritical approximation of the Sobolev quotient and a related concentration result ⋮ A non-linear problem involving a critical Sobolev exponent ⋮ Equivalent Moser type inequalities in $\mathbb{R}^2$ and the zero mass case ⋮ Fractional Sobolev, Moser-Trudinger, Morrey-Sobolev inequalities under Lorentz norms ⋮ The existence of three solutions for $p$-Laplacian problems with critical and supercritical growth ⋮ Solution to biharmonic equation with vanishing potential ⋮ Existence of nontrivial solutions for $p$-Laplacian-like equations ⋮ Multiple solutions for a semilinear elliptic equation with critical growth and magnetic field ⋮ Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems ⋮ Elliptic systems involving multiple critical nonlinearities and symmetric multi-polar potentials ⋮ Infinitely many sign-changing solutions for the Brézis-Nirenberg problem ⋮ Positive symmetric solutions for a class of critical quasilinear elliptic problems in $\mathbb R^N$ ⋮ Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality ⋮ Ground states of time-harmonic semilinear Maxwell equations in $\mathbb R^3$ with vanishing permittivity ⋮ A critical fractional equation with concave-convex power nonlinearities ⋮ Polyharmonic equations with critical exponential growth in the whole space $\mathbb{R}^{n}$ ⋮ Existence of solutions for a class of $p$-Laplacian type equation with critical growth and potential vanishing at infinity ⋮ Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities ⋮ Infinitely many solutions for the spinorial Yamabe problem on the round sphere ⋮ Quasilinear elliptic systems involving critical Hardy-Sobolev and Sobolev exponents ⋮ Sharp subcritical and critical Trudinger-Moser inequalities on $\mathbb{R}^{2}$ and their extremal functions ⋮ Concentration-compactness principle for nonlocal scalar field equations with critical growth ⋮ Yamabe-type equations on Carnot groups ⋮ Blow-up analysis concerning singular Trudinger-Moser inequalities in dimension two ⋮ Positive symmetric results for a weighted quasilinear elliptic system with multiple critical exponents in $\mathbb{R}^{N}$ ⋮ On ground state solutions for a Kirchhoff type equation with critical growth ⋮ The blow-up of critical anisotropic equations with critical directions ⋮ On a singular and nonhomogeneous $N$-Laplacian equation involving critical growth ⋮ On the elliptic problems involving multisingular inverse square potentials and concave-convex nonlinearities ⋮ Geometric methods for nonlinear many-body quantum systems ⋮ Generalized $n$-Laplacian: quasilinear nonhomogeneous problem with critical growth ⋮ Multiple positive solutions for semilinear elliptic equations involving multi-singular inverse square potentials and concave-convex nonlinearities ⋮ Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Three positive solutions for a semilinear elliptic equation in $\mathbb R^N$ involving sign-changing weight ⋮ Exponential elliptic boundary value problems on a solid torus in the critical of supercritical case ⋮ A class of $p$-$q$-Laplacian type equation with concave-convex nonlinearities in bounded domain ⋮ Existence of nonnegative solutions for quasilinear elliptic equations with indefinite critical nonlinearities ⋮ Minimizers to Rayleigh quotients of critical elliptic systems involving different Hardy-type terms ⋮ Infinitely many solutions for an elliptic problem with double critical Hardy-Sobolev-Maz'ya terms ⋮ $n$-Kirchhoff type equations with exponential nonlinearities ⋮ Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents ⋮ Spike solutions of a nonlinear Schrödinger equation with degenerate potential ⋮ A theorem about representation of Palais-Smale sequence and its applications ⋮ A compactness theorem for weak solutions of higher-dimensional $H$-systems ⋮ Compactness via symmetrization ⋮ Critical points at infinity in a fourth order elliptic problem with limiting exponent ⋮ On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term ⋮ Global homoclinic bifurcation for damped systems ⋮ Pseudoholomorphic curves and multiplicity of homoclinic orbits ⋮ The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds ⋮ A class of solutions for the Neumann problem $-\Delta u+ \lambda u= u^{(N+2)/ (N-2)}$ ⋮ Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents ⋮ A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space ⋮ Homoclinic orbits on compact hypersurfaces in $\mathbb{R}^{2N}$, of restricted contact type ⋮ Some sufficient conditions for the existence of positive solutions to the equation $-\Delta u + a(x)u = u^{2^* -1}$ in bounded domains ⋮ Critical $p$-Laplacian problems in $\mathbf R^ N$ ⋮ An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension ⋮ Existence and multiplicity of symmetric solutions for a class of singular elliptic problems ⋮ Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere ⋮ Adams' inequality and limiting Sobolev embeddings into Zygmund spaces ⋮ Infinitely many small solutions for the $ p (x)$-Laplacian operator with nonlinear boundary conditions ⋮ Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs ⋮ Existence and multiplicity results for the prescribed Webster scalar curvature problem on three CR manifolds ⋮ Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions ⋮ The scalar-curvature problem on higher-dimensional spheres ⋮ Singular minimization problems ⋮ On critical Kirchhoff problems driven by the fractional Laplacian ⋮ Existence and non-existence results for fractional Kirchhoff Laplacian problems ⋮ Existence and concentration of positive solutions for a critical $p$\&$q$ equation ⋮ Supercritical Moser-Trudinger inequalities and related elliptic problems ⋮ Existence problems on Heisenberg groups involving Hardy and critical terms ⋮ On a critical Kirchhoff-type problem ⋮ Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains ⋮ Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights ⋮ Continuity and canceling operators of order $n$ on $\mathbb{R}^n$ ⋮ Properties of solutions to semilinear elliptic problem with Hardy potential ⋮ Remarks about a generalized pseudo-relativistic Hartree equation ⋮ Improved Moser-Trudinger inequality of Tintarev type in dimension $n$ and the existence of its extremal functions ⋮ New weighted sharp Trudinger-Moser inequalities defined on the whole euclidean space $\mathbb{R}^N$ and applications ⋮ Saddle solutions for the critical Choquard equation ⋮ Existence and nonexistence of nontrivial solutions for critical biharmonic equations ⋮ Existence of solutions for Kirchhoff type systems involving $Q$-Laplacian operator in Heisenberg group ⋮ Extremal problems of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds ⋮ Stein-Weiss inequalities with the fractional Poisson kernel ⋮ An existence result for $( p , q )$-Laplace equations involving sandwich-type and critical growth ⋮ Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity ⋮ Sign-changing solutions to elliptic problems with two critical Sobolev-Hardy exponents ⋮ Quasilinear elliptic problems with critical exponents and Hardy terms ⋮ On nonlocal existence results for elliptic equations with convex-concave nonlinearities ⋮ Multiple blowing-up solutions to critical elliptic systems in bounded domains ⋮ Multiple solutions for critical fourth-order elliptic equations of Kirchhoff type ⋮ On bi-nonlocal problem for elliptic equations with Neumann boundary conditions ⋮ Second-order elliptic equation with singularities ⋮ Improved results on planar Kirchhoff-type elliptic problems with critical exponential growth ⋮ Maximizers for the variational problems associated with Sobolev type inequalities under constraints ⋮ Weakly localized states for nonlinear Dirac equations ⋮ Concentration and energy invariance for a class of fully nonlinear elliptic equations ⋮ Nonlocal problems with critical Hardy nonlinearity ⋮ Nonlinear Choquard equations with Hardy-Littlewood-Sobolev critical exponents ⋮ The concentration-compactness principles for $W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)$ and application ⋮ Palais-Smale sequences for the fractional CR Yamabe functional and multiplicity results ⋮ Nondegeneracy of ground states and multiple semiclassical solutions of the Hartree equation for general dimensions ⋮ Existence of solutions for the double phase variational problems without AR-condition ⋮ Three solutions for a nonlocal problem with critical growth ⋮ Three solutions of a Kirchhoff type problem involving critical growth and near resonance ⋮ Asymmetric critical $p$-Laplacian problems ⋮ On a class of critical $p$-biharmonic Kirchhoff type problems with indefinite weights ⋮ Nonlocal Kirchhoff problems with singular exponential nonlinearity ⋮ Multiple positive solutions to critical p-Laplacian equations with vanishing potential ⋮ Existence for fractional $(p,q)$ systems with critical and Hardy terms in $\mathbb{R}^N$ ⋮ The compactness and the concentration compactness via $P$-capacity ⋮ The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions ⋮ A concentration-compactness lemma with applications to singular eigenvalue problems ⋮ Some properties of the potential-to-ground state map in quantum mechanics ⋮ A nonhomogeneous and critical Kirchhoff-Schrödinger type equation in $\mathbb{R}^4$ involving vanishing potentials ⋮ Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in $\mathbb{R}^2$ ⋮ Maximal non-compactness of Sobolev embeddings ⋮ On the critical Neumann problem with weight in exterior domains. ⋮ Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms ⋮ Divergent operator with degeneracy and related sharp inequalities ⋮ A minimization problem involving a critical Sobolev exponent and its related Euler-Lagrange equation ⋮ On the prescribed scalar curvature problem on 4-manifolds ⋮ Existence and multiplicity results for heteroclinic orbits of second order Hamiltonian systems ⋮ A log-exp elliptic equation in the plane ⋮ Singular Moser-Trudinger inequality involving $L^n$ norm in the entire Euclidean space ⋮ Elliptic problems in the half-space with nonlinear critical boundary conditions ⋮ Solutions of Hartree-Fock equations for Coulomb systems ⋮ A modified singular Trudinger-Moser inequality ⋮ A critical concave-convex Kirchhoff-type equation in $\mathbb{R}^4$ Involving potentials which may vanish at infinity ⋮ Existence of bound and ground states for an elliptic system with double criticality ⋮ Singular weighted sharp Trudinger-Moser inequalities defined on $\mathbb{R}^N$ and applications to elliptic nonlinear equations ⋮ Infinitely many solutions for a class of critical Kirchhoff-type equations involving $p$-Laplacian operator ⋮ Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type ⋮ Existence of positive solutions for a problem with lack of compactness involving the $p$-Laplacian ⋮ Existence results for some nonlinear elliptic system with lack of compactness ⋮ Soliton solutions for quasilinear Schrödinger equations. II. ⋮ Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation. ⋮ Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents ⋮ On a class of singular biharmonic problems involving critical exponents. ⋮ The asymptotic behaviour of the ground state solutions for Hénon equation. ⋮ Asymptotic estimates and blow-up theory for critical equations involving the $p$-Laplacian ⋮ Extremal functions for Trudinger-Moser inequalities with nonnegative weights ⋮ Sharp Sobolev asymptotics for critical anisotropic equations ⋮ On a fourth-order quasilinear elliptic equation of concave-convex type ⋮ Effect of topology on the multiplicity of solutions for some semilinear elliptic systems with critical Sobolev exponent ⋮ Energy bounds for entire nodal solutions of autonomous superlinear equations ⋮ A sharp form of Moser-Trudinger inequality in high dimension ⋮ Hardy-Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients ⋮ $p$-Laplacian problems with critical Sobolev exponents ⋮ Localization of solutions for nonlinear elliptic problems with critical growth ⋮ Moser-Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2 ⋮ Critical singular problems via concentration-compactness lemma ⋮ Positive solutions to a Neumann problem of semilinear elliptic system with critical nonlinearity ⋮ Degenerate elliptic inequalities with critical growth ⋮ A global multiplicity result for $N$-Laplacian with critical nonlinearity of concave-convex type ⋮ The Paneitz curvature problem on lower-dimensional spheres ⋮ Blow-up results and global existence of positive solutions for the inhomogeneous evolution $p$-Laplacian equations ⋮ Quasilinear elliptic systems with critical Sobolev exponents in $\mathbb {R}^N$ ⋮ Positive solutions for some quasilinear equations with critical and supercritical growth ⋮ On the elliptic problems involving multi-singular inverse square potentials and multi-critical Sobolev-Hardy exponents ⋮ Moser--Trudinger inequality for functions with mean value zero ⋮ The sharp quantitative Sobolev inequality for functions of bounded variation ⋮ Positive minimizers of the best constants and solutions to coupled critical quasilinear systems ⋮ Standing waves for a class of Kirchhoff type problems in $\mathbb R^3$ involving critical Sobolev exponents ⋮ Regularity of the obstacle problem for the parabolic biharmonic equation ⋮ An improved singular Trudinger-Moser inequality in unit ball ⋮ Higher-order functional inequalities related to the clamped 1-biharmonic operator ⋮ Hamiltonian elliptic systems involving nonlinear Schrödinger equations with critical growth ⋮ A note on a nonlinear elliptic problem with a nonlocal coefficient ⋮ On degenerate $p(x)$-Laplace equations involving critical growth with two parameters ⋮ Solutions to Kirchhoff equations with critical exponent ⋮ Concentrating ground-state solutions for a class of Schödinger-Poisson equations in $\mathbb{R}^3$ involving critical Sobolev exponents ⋮ Existence of multiple nontrivial solutions for a $p$-Kirchhoff type elliptic problem involving sign-changing weight functions ⋮ Un phénomène de concentration évanescente pour des flots non- stationnaires incompressibles en dimension deux. (A concentration- concellation phenomenon for nonstationary incompressible flows in two dimensions) ⋮ Higher order singular problems of Caffarelli-Kohn-Nirenberg-Lin type ⋮ Multiplicity of solutions for homogeneous elliptic systems with critical growth ⋮ Exponential problem on a compact Riemannian manifold without boundary ⋮ The concentration-compactness principle in the calculus of variations. The locally compact case. II ⋮ Existence of positive solutions of the equation $-\Delta u+a(x)u=u^{(N+2)/(N-2)}$ in ${\mathbb{R}}^ N$ ⋮ Proof of two conjectures of H. Brezis and L. A. Peletier ⋮ Existence of multiple positive solutions to singular elliptic systems involving critical exponents ⋮ Quasilinear asymptotically periodic elliptic equations with critical growth ⋮ Existence and nonexistence of maximizers for variational problems associated with Trudinger--Moser type inequalities in ${\mathbb{R}^N}$ ⋮ Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger-Poisson systems in $\mathbb R^3$ ⋮ Existence, non-existence and regularity of radial ground states for $p$-Laplacian equations with singular weights ⋮ Existence of nontrivial solutions for quasilinear elliptic equations at critical growth ⋮ A nonhomogeneous elliptic problem involving critical growth in dimension two ⋮ The critical Neumann problem for semilinear elliptic equations with concave perturbations ⋮ Existence of a ground state solution for a nonlinear scalar field equation with critical growth ⋮ Symmetry analysis of the bidimensional Lane-Emden systems ⋮ Existence of maximizers for Sobolev-Strichartz inequalities ⋮ Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space ⋮ Existence and multiplicity of solutions to equations of $N$-Laplacian type with critical exponential growth in $\mathbb R^N$ ⋮ Bahri-Coron type theorem for the scalar curvature problem on high dimensional spheres ⋮ Quasilinear elliptic system with coupling on nonhomogeneous critical term ⋮ Existence of infinitely many weak solutions for the $p$-Laplacian with nonlinear boundary conditions ⋮ Multiple solutions for a Hénon-like equation on the annulus ⋮ Asymptotic behavior of solutions for Hénon systems with nearly critical exponent ⋮ On a critical Neumann problem with a perturbation of lower order ⋮ Asymptotic behaviors of a class of $N$-Laplacian Neumann problems with large diffusion ⋮ Best constants in Sobolev inequalities on manifolds with boundary in the presence of symmetries and applications ⋮ Ground state for a coupled elliptic system with critical growth ⋮ On some nonlinear partial differential equations involving the 1-Laplacian ⋮ On the singular critical quasilinear problems in $\mathbb R^N$ ⋮ Some remarks on systems of elliptic equations doubly critical in the whole $\mathbb R^N$ ⋮ Nontrivial solutions to semilinear elliptic problems involving two critical Hardy-Sobolev exponents ⋮ Multiplicity of solutions for the noncooperative $p(x)$-Laplacian operator elliptic system involving the critical growth ⋮ Compact embeddings and indefinite semilinear elliptic problems ⋮ Concentration compactness principle at infinity with partial symmetry and its application ⋮ A sharp form of trace Moser-Trudinger inequality on compact Riemannian surface with boundary ⋮ Schrödinger equations with critical nonlinearity, singular potential and a ground state ⋮ Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent ⋮ On the compactness problem of extremal functions to sharp Riemannian $L^p$-Sobolev inequalities ⋮ Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption ⋮ Extremal of log Sobolev inequality and $W$ entropy on noncompact manifolds ⋮ Solutions for a Kirchhoff equation with critical Caffarelli-Kohn-Nirenberg growth and discontinuous nonlinearity ⋮ Sharp Hardy inequalities on the solid torus ⋮ On Trudinger-Moser type inequalities involving Sobolev-Lorentz spaces ⋮ Adams' inequalities for bi-Laplacian and extremal functions in dimension four ⋮ The heat flow with a critical exponential nonlinearity ⋮ On a quasilinear nonhomogeneous elliptic equation with critical growth in $\mathbb R^N$ ⋮ On a $p$-Laplace equation with multiple critical nonlinearities ⋮ Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions ⋮ The homogeneous Hénon-Lane-Emden system ⋮ On the Neumann problem for an elliptic system with weights and multiple critical nonlinearities ⋮ Topological and analytical properties of Sobolev bundles. I: The critical case ⋮ Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds ⋮ A sharpened Moser-Pohozaev-Trudinger inequality with mean value zero in $\mathbb R^2$ ⋮ The div-curl lemma ``trente ans après: an extension and an application to the $G$-convergence of unbounded monotone operators ⋮ Extremal functions and best constants to an inequality involving Hardy potential and critical Sobolev exponent ⋮ Positive solutions to the weighted critical quasilinear problems ⋮ Elliptic systems involving the critical exponents and potentials ⋮ Ground state solution for quasilinear elliptic equation with critical growth in $\mathbb R^N$ ⋮ On the existence of ground state solutions to nonlinear Schrödinger equations with multisingular inverse-square anisotropic potentials ⋮ On the weighted elliptic problems involving multi-singular potentials and multi-critical exponents ⋮ Improved singular Moser-Trudinger inequalities and their extremal functions ⋮ Multiple solutions to polyharmonic elliptic problem involving GJMS operator on compact manifolds ⋮ Existence of solutions to fractional $p$-Laplacian systems with homogeneous nonlinearities of critical Sobolev growth ⋮ The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems ⋮ A variational approach to homoclinic orbits in Hamiltonian systems ⋮ Cocompact embedding theorem for functions of bounded variation into Lorentz spaces ⋮ Hardy-Sobolev inequalities with distance to the boundary weight functions ⋮ On critical N‐Kirchhoff type equations involving Trudinger–Moser nonlinearity ⋮ Soliton resolution for the energy-critical nonlinear wave equation in the radial case ⋮ A singular Liouville equation on planar domains ⋮ Least energy solutions to quasilinear subelliptic equations with constant and degenerate potentials on the Heisenberg group ⋮ Integral inequalities with an extended Poisson kernel and the existence of the extremals ⋮ Existence and multiplicity results for a multiparameter quasilinear Schrödinger equation ⋮ Multiple solutions for a class of generalized critical noncooperative Schrödinger systems in $\mathbb{R}^N$ ⋮ On a weighted trace embedding and applications to critical boundary problems^† ⋮ Nonlinear elliptic systems involving Hardy-Sobolev criticalities ⋮ On a quaternary nonlocal isoperimetric problem ⋮ Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs ⋮ Fourth order Hardy-Sobolev equations: singularity and doubly critical exponent ⋮ Existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials ⋮ Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $\mathbb{R}^2$ ⋮ Bubble decomposition for the harmonic map heat flow in the equivariant case ⋮ The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order ⋮ Solutions for a quasilinear Schrödinger equation: Subcritical and critical cases ⋮ Fine properties of symmetric and positive matrix fields with bounded divergence ⋮ Multiple positive solutions to a class of modified nonlinear Schrödinger equation in a high dimension ⋮ Existence of positive solution for a class of elliptic problems with indefinite nonlinearities with critical and supercritical growth ⋮ A perturbed fractional p-Kirchhoff problem with critical nonlinearity ⋮ Non local weighted fourth order equation in dimension $4$ with non-linear exponential growth ⋮ Existence of positive solutions for a class of elliptic problems with fast increasing weights and critical exponent discontinuous nonlinearity ⋮ The ground states of quasilinear Hénon equation with double weighted critical exponents ⋮ Existence of solution for magnetic Schrödinger equation with the Neumann boundary condition ⋮ Existence and multiplicity of solutions to N-Kirchhoff equations with critical exponential growth and a perturbation term ⋮ Existence of solutions for a class of quasilinear equations with vanishing potentials ⋮ Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth ⋮ On a weighted Adams type inequality and an application to a biharmonic equation ⋮ An improved Trudinger-Moser inequality involving $N$-Finsler-Laplacian and $L^p$ norm ⋮ Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds ⋮ Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities ⋮ Existence and properties of radial solutions to critical elliptic systems involving strongly coupled Hardy terms ⋮ Zero-mass gauged Schrödinger equations with supercritical exponential growth ⋮ Trudinger–Moser‐type inequality with logarithmic convolution potentials ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application ⋮ Ground state solutions for a Kirchhoff‐type elliptic system involving critical exponential growth nonlinearities ⋮ Extremal sections for a Trudinger-Moser functional on vector bundle over a closed Riemann surface ⋮ Normalized Solutions for Schrödinger Equations with Critical Exponential Growth in $\boldsymbol{\mathbb{R}^2}$ ⋮ Elliptic problem involving logarithmic weight under exponential nonlinearities growth ⋮ Multiplicity results for generalized quasilinear critical Schrödinger equations in $\mathbb{R}^N$ ⋮ Multiplicity of solutions for Schrödinger-Bopp-Podolsky systems ⋮ A sharp Moser-Trudinger type inequality involving $L^p$ norm in $\mathbb{R}^n$ with degenerate potential ⋮ Weighted Elliptic Equations in Dimension N with Subcritical and Critical Double Exponential Nonlinearities ⋮ Positive solutions to the planar logarithmic Choquard equation with exponential nonlinearity ⋮ Signed and sign-changing solutions to the nonlinear Choquard problem with upper critical exponent ⋮ Bound and ground states of coupled ``NLS-KdV equations with Hardy potential and critical power ⋮ Existence and multiplicity of solutions for a class of Helmholtz systems ⋮ Radial solutions to critical elliptic systems involving $p$-Laplacian and different Hardy-type terms ⋮ Blow-up behavior of solutions to critical Hartree equations on bounded domain ⋮ Multiple solutions of $p$-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents ⋮ Existence of solution for a class of variational inequality in whole $\mathbb{R}^N$ with critical growth: the local mountain pass case ⋮ The Neumann problem for a class of generalized Kirchhoff-type potential systems ⋮ Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals ⋮ Coron's problem for the critical Lane-Emden system ⋮ A system with weights and with critical Sobolev exponent ⋮ One-scale H-distributions and variants ⋮ Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion ⋮ Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type ⋮ The Brezis–Nirenberg problem for fractional systems with Hardy potentials ⋮ Kirchhoff type elliptic equations with double criticality in Musielak–Sobolev spaces ⋮ A Choquard‐type equation with a singular absorption nonlinearity in two dimensions ⋮ Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth ⋮ Existence of solutions for a nonlocal elliptic system with critical and subcritical exponential growth ⋮ Anisotropic Moser-Trudinger inequality involving $L^n$ norm in the entire space $\mathbb{R}^n$ ⋮ Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in $\mathbb{R}^N$ ⋮ A multiplicity result to Schr\"{o}dinger Equation with singular points ⋮ Local uniqueness and non-degeneracy of bubbling solution for critical Hamiltonian system ⋮ The multiplicity of solutions for the critical problem involving the fracional p-Laplacian operator ⋮ On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces ⋮ A class of critical $p$-Kirchhoff type equations on closed manifolds ⋮ Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent ⋮ Multiplicity of nontrivial solutions for p‐Kirchhoff type equation with Neumann boundary conditions ⋮ Multiple positive solutions for Kirchhoff-type problems involving supercritical and critical terms ⋮ A fourth order elliptic equation with nonlinear boundary conditions ⋮ On the Neumann problem of Hardy-Sobolev critical equations with the multiple singularities ⋮ A free boundary problem involving limiting Sobolev exponents ⋮ Non-existence of extremals for the Adimurthi-Druet inequality ⋮ A direct variational approach to Skyrme's model for meson fields ⋮ On a variational problem with lack of compactness: The topological effect of the critical points at infinity ⋮ Schrödinger-Kirchhoff equation involving double critical nonlinearities ⋮ Some remarks on Sobolev type inequalities ⋮ A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,n}$ ⋮ Existence of symmetric solutions for the Skyrme's problem ⋮ Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents ⋮ Ground state and multiple solutions for the fractional Schrödinger-Poisson system with critical Sobolev exponent ⋮ Homoclinics and heteroclinics for a class of conservative singular Hamiltonian systems ⋮ Best constant in weighted Sobolev inequality ⋮ Multiple positive and sign-changing solutions of an elliptic equation with fast increasing weight and critical growth ⋮ Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg groups and existence of ground state solutions ⋮ Multiple homoclinics for a class of singular Hamiltonian systems ⋮ Existence and non-existence results for variational higher order elliptic systems ⋮ Positive solutions for a Schrödinger-Poisson system involving concave-convex nonlinearities ⋮ Concentration phenomena for critical fractional Schrödinger systems ⋮ Critical points of embeddings of $H_ 0^{1,n}$ into Orlicz spaces ⋮ Concentration compactness for the critical Maxwell-Klein-Gordon equation ⋮ Multiplicity results for degenerate fractional $p$-Laplacian problems with critical growth ⋮ Holes and obstacles ⋮ Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in $\mathbb{R}^4$ ⋮ Concentration-compactness principle of singular Trudinger-Moser inequalities in $\mathbb{R}^n$ and $n$-Laplace equations ⋮ Some sharp inequalities related to Trudinger-Moser inequality ⋮ Compactness theorems for spaces of functions with bounded derivatives and applications to limit analysis problems in plasticity ⋮ On the existence of infinitely many solutions for nonlocal systems with critical exponents ⋮ On conformal scalar curvature equations in ${\mathbb{R}}^ n$ ⋮ Existence and multiplicity of solutions for critical Kirchhoff-type $p$-Laplacian problems ⋮ Decay estimates for fourth order wave equations ⋮ Remarks about a fractional Choquard equation: ground state, regularity and polynomial decay ⋮ Bifurcation results for problems with fractional Trudinger-Moser nonlinearity ⋮ The existence and concentration of ground-state solutions for a class of Kirchhoff type problems in ${\mathbb{R}^{3}}$ involving critical Sobolev exponents ⋮ Multiple homoclinic solutions for a class of autonomous singular systems in $\mathbb{R}^2$ ⋮ Multiplicity of solutions for singular quasilinear Schrödinger equations with critical exponents ⋮ Existence and multiplicity of positive solutions for Neumann problems involving singularity and critical growth ⋮ Best constants in Sobolev trace inequalities ⋮ Prescribing the scalar curvature problem on the four-dimensional half sphere ⋮ Bahri invariants for fractional Nirenberg-type flows ⋮ Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities ⋮ Existence and multiplicity for quasi-critical fourth order quasilinear problems with generalized vanishing potentials ⋮ Multiscale weak compactness in metric spaces ⋮ Nonlocal Neumann problem with critical exponent from the point of view of the trace ⋮ Nodal solutions for $p$-Laplace equations with critical growth. ⋮ Best constants in second-order Sobolev inequalities on Riemannian manifolds and applications. ⋮ Global, decaying solutions of a focusing energy-critical heat equation in $\mathbb{R}^4$ ⋮ Sharp Sobolev inequalities of second order ⋮ Existence and multiplicity of solutions for Hardy nonlocal fractional elliptic equations involving critical nonlinearities ⋮ A convex-concave problem with a nonlinear boundary condition. ⋮ Nonlinear Liouville theorems for some critical problems on $H$-type groups. ⋮ An elliptic problem with critical growth in domains with shrinking holes. ⋮ Multiple symmetric results for quasilinear elliptic systems involving singular potentials and critical Sobolev exponents in $\mathbb{R}^N$ ⋮ Gradient stability for the Sobolev inequality: the case $p\geq 2$ ⋮ Regularity and classification of solutions to static Hartree equations involving fractional Laplacians ⋮ Multiple solutions for a critical Kirchhoff system ⋮ A fractional elliptic problem in $\mathbb {R}^n$ with critical growth and convex nonlinearities ⋮ The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem ⋮ Positive solutions for a class of singular quasilinear Schrödinger equations with critical Sobolev exponent ⋮ Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in $\mathbb R^N$ ⋮ Existence of positive solution of the equation $(-\Delta )^{s}u+a(x)u=|u|^{2^{*}_{s}-2}u$ ⋮ A critical fractional $p$-Kirchhoff type problem involving discontinuous nonlinearity ⋮ A concentration-compactness principle for sequences of Riemannian surfaces. ⋮ Concentration-compactness for singular nonlocal Schrödinger equations with oscillatory nonlinearities ⋮ Variational identities and applications to differential systems ⋮ Ground state solution for a class of indefinite variational problems with critical growth ⋮ Localization of directed polymers with general reference walk ⋮ A nonexistence result for a nonlinear equation involving critical Sobolev exponent ⋮ Sharp Adams-type inequality invoking Hardy inequalities ⋮ Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation ⋮ Multiple solutions for a Kirchhoff equation with critical growth ⋮ Extremal functions for an embedding from some anisotropic space, involving the ``one Laplacian ⋮ An ODE approach to the equation $\Delta u + Ku^{{n+2}\over{n-2}}=0$ in $\mathbb{R}^ n$ ⋮ Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ⋮ Generalized Lyapunov inequalities involving critical Sobolev exponents ⋮ Nehari manifold and existence of positive solutions to a class of quasilinear problems ⋮ Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents ⋮ A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb R^2$ ⋮ Multiple minimal nodal solutions for a quasilinear Schrödinger equation with symmetric potential ⋮ The scalar curvature problem on the four dimensional half sphere ⋮ Some existence results for a paneitz type problem via the theory of critical points at infinity ⋮ Hardy inequalities and some critical elliptic and parabolic problems ⋮ Critical phenomena in linear elliptic problems ⋮ Some general forms of sharp Sobolev inequalities ⋮ On multiple solutions of quasilinear equations involving the critical Sobolev exponent ⋮ Concentration of low energy extremals ⋮ Multiple solutions for the $p$-Laplace operator with critical growth ⋮ Global compactness properties of semilinear elliptic equations with critical exponential growth ⋮ Best constant in critical Sobolev inequalities of second-order in the presence of symmetries ⋮ Quasilinear Dirichlet problems in $\mathbb R^N$ with critical growth. ⋮ A sharp inequality for Sobolev functions ⋮ Concentration around a sphere for a singularly perturbed Schrödinger equation ⋮ Elliptic equations in dimension three: A conjecture of H. Brezis ⋮ On some fourth-order semilinear elliptic problems in $\mathbb R^N$ ⋮ Elliptic equations of fourth-order with critical exponents on compact Riemannian manifolds ⋮ Looking for the Bernoulli shift ⋮ Asymptotics of solutions for fully nonlinear elliptic problems at nearly critical growth ⋮ Existence theorems for equations involving the 1-Laplacian: first eigenvalues for $-\Delta_1$ ⋮ Multiple solutions to the Plateau problem for nonconstant mean curvature ⋮ On $G$-invariant solutions of a singular biharmonic elliptic system involving multiple critical exponents in $R^N$ ⋮ Existence of multiple solutions for a quasilinear Neumann problem with critical exponent ⋮ Multiplicity of solutions for a quasilinear elliptic equation with $(p,q)$-Laplacian and critical exponent on $\mathbb{R}^N$ ⋮ Existence of solution for a quasilinear elliptic Neumann problem involving multiple critical exponents ⋮ Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six ⋮ Existence and multiplicity of solutions for Schrödinger equations with asymptotically linear nonlinearities allowing interaction with essential spectrum ⋮ Fitzhugh-Nagumo system with zero mass and critical growth ⋮ Nonlocal Hénon equation with nonlinearities involving Sobolev critical and supercritical growth ⋮ Planar Schrödinger-Poisson system with critical exponential growth in the zero mass case ⋮ On elliptic equations with Stein-Weiss type convolution parts ⋮ Planar Schrödinger-Choquard equations with potentials vanishing at infinity: the critical case ⋮ Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6 ⋮ Multiplicity of solutions for Schrödinger-Poisson system with critical exponent in $\mathbb{R}^3$ ⋮ Existence and multiplicity of positive solutions to a $p$-Kirchhoff-type equation ⋮ The existence of a nontrivial weak solution to a double critical problem involving a fractional Laplacian in $\mathbb{R}^N$ with a Hardy term ⋮ Aubin type almost sharp Moser-Trudinger inequality revisited ⋮ Existence to fractional critical equation with Hardy-Littlewood-Sobolev nonlinearities ⋮ Critical gauged Schrödinger equations in $\mathbb{R}^2$ with vanishing potentials ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Profile decomposition in Sobolev spaces and decomposition of integral functionals. I: Inhomogeneous case ⋮ Existence of minimizers for a generalized liquid drop model with fractional perimeter ⋮ Asymptotic properties of an optimal principal eigenvalue with spherical weight and Dirichlet boundary conditions ⋮ Estimate for concentration level of the Adams functional and extremals for Adams-type inequality ⋮ A note on prescribed Q-curvature ⋮ Kirchhoff type elliptic systems with exponential growth nonlinearities ⋮ Existence and multiplicity results for fractional Schrödinger equation with critical growth ⋮ Rigidity estimates for isometric and conformal maps from $\mathbb{S}^{n-1}$ to $\mathbb{R}^n$ ⋮ Maximization problem on Trudinger-Moser inequality involving Lebesgue norm ⋮ Adams-Moser-Trudinger inequality in the Cartesian product of Sobolev spaces and its applications ⋮ Positive solutions of semipositone elliptic problems with critical Trudinger-Moser nonlinearities ⋮ Fractional Hardy-Sobolev elliptic problems ⋮ Positive solutions of Kirchhoff-hénon type elliptic equations with critical Sobolev growth ⋮ The endpoint distribution of directed polymers ⋮ Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two ⋮ Multiplicity of solutions to the generalized extensible beam equations with critical growth ⋮ Concentration-compactness principle for Trudinger-Moser inequalities with logarithmic weights and their applications ⋮ Improved Sobolev inequalities and critical problems ⋮ Classification to the positive radial solutions with weighted biharmonic equation ⋮ On the singular second-order elliptic equation ⋮ Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure ⋮ Multiplicity of positive solutions for a class of $p$-Kirchhoff equation with critical exponent ⋮ Extremal for a $k$-Hessian inequality of Trudinger-Moser type ⋮ Existence and asymptotic behaviour of solutions for a quasi-linear Schrödinger-Poisson system with a critical nonlinearity ⋮ A Hardy-Trudinger-Moser inequality involving $L^p$ norm in the hyperbolic space ⋮ Energy estimates on existence of extremals for Trudinger-Moser inequalities ⋮ Fractional $p \& q$ Laplacian problems in $\mathbb{R}^N$ with critical growth ⋮ Singular supercritical Trudinger-Moser inequalities and the existence of extremals ⋮ Symmetry and compact embeddings for critical exponents in metric-measure spaces ⋮ Existence of solutions to elliptic problems with fractional p-Laplacian and multiple critical nonlinearities in the entire space $\mathbb{R}^N$ ⋮ Quantitative stability for the Heisenberg-Pauli-Weyl inequality ⋮ Extremals for the singular Moser-Trudinger inequality via n-harmonic transplantation ⋮ Existence of nontrivial solution for a quasilinear elliptic equation with $(p, q)$-Laplacian in $\mathbb{R}^N$ involving critical Sobolev exponents ⋮ Existence and nonexistence results for elliptic equations involving two critical singular nonlinearities at the same pole ⋮ Multi-bump analysis for Trudinger-Moser nonlinearities I. Quantification and location of concentration points ⋮ Multiplicity results for $(p, q)$-Laplacian equations with critical exponent in $\mathbb{R}^N$ and negative energy ⋮ Sharp weighted Trudinger-Moser inequalities with the $L^n$ norm in the entire space $\mathbb{R}^n$ and existence of their extremal functions ⋮ Optimizers of the Sobolev and Gagliardo-Nirenberg inequalities in $\dot{W}^{s,p} $ ⋮ More insights into the Trudinger-Moser inequality with monomial weight ⋮ The first GJMS invariant ⋮ Extremals for Hardy-Sobolev type inequalities with monomial weights ⋮ On a critical Schrödinger system involving Hardy terms ⋮ Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations ⋮ Energy quantization for a singular super-Liouville boundary value problem ⋮ Fractional Kirchhoff-Schrödinger equation with critical exponential growth in $\mathbb{R}^N$ ⋮ A Paneitz-Branson type equation with Neumann boundary conditions ⋮ Concentration-compactness principle for Trudinger-Moser's inequalities on Riemannian manifolds and Heisenberg groups: a completely symmetrization-free argument ⋮ The existence of extremal functions for discrete Sobolev inequalities on lattice graphs ⋮ Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes ⋮ Positive solutions to a fourth-order elliptic problem by the Lusternik-Schnirelmann category ⋮ Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent ⋮ Nonlinear Schrödinger equation with unbounded or decaying radial potentials involving exponential critical growth in $\mathbb R^2$ ⋮ Multiplicity results for semilinear heterogeneous problems in exterior domains of $\mathbb{R}^2$ involving subcritical or critical nonlinearities à la Trudinger-Moser ⋮ Nonlocal elliptic equation with critical exponential growth and resonance in high-order eigenvalues ⋮ A singular problem with nonlinearities of exponential growth ⋮ A weighted Trudinger-Moser inequality on a closed Riemann surface with a finite isometric group action ⋮ Normalized ground states of nonlinear biharmonic Schrödinger equations with Sobolev critical growth and combined nonlinearities ⋮ Existence and multiplicity of solutions to a Kirchhoff type elliptic system with Trudinger-Moser growth ⋮ The ground state solutions for Kirchhoff-Schrödinger type equations with singular exponential nonlinearities in $\mathbb{R}^N$ ⋮ Singular quasilinear critical Schrödinger equations in $\mathbb{R}^N$ ⋮ Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on $\mathbb{S}^n$ ⋮ Critical equations with Hardy terms in the Heisenberg group ⋮ Vector analysis on symmetric manifolds and Sobolev inequalities ⋮ On a weighted elliptic equation of $N$-Kirchhoff type with double exponential growth ⋮ Mountain-pass type solutions for the Chern-Simons-Schrödinger equation with zero mass potential and critical exponential growth ⋮ Existence and multiplicity of positive solutions for a class of critical fractional Laplacian systems ⋮ Some weighted fourth-order Hardy-Hénon equations ⋮ Non simple blow ups for the Nirenberg problem on half spheres ⋮ A lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,\gamma}$, $\gamma > 1$ ⋮ On a nonlinear elliptic fractional problem under mixed boundary condition: effect of the geometry of the domain ⋮ On the existence of optimizers for time-frequency concentration problems ⋮ Critical Schrödinger equations with Stein-Weiss convolution parts in $\mathbb{R}^2$ ⋮ Analysis of a low linear perturbed Choquard equation with critical growth ⋮ On the generalised Brézis-Nirenberg problem ⋮ Infinitely many solutions for fractional elliptic systems involving critical nonlinearities and Hardy potentials ⋮ Existence and asymptotic properties of positive solutions for a general quasilinear Schrödinger equation ⋮ Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents ⋮ Existence of positive ground state solutions of Schrödinger-Poisson system involving negative nonlocal term and critical exponent on bounded domain ⋮ Existence of a positive solution for a class of non-local elliptic problem with critical growth in $\mathbb{R}^N$ ⋮ On symmetric solutions for $(p, q)$-Laplacian equations in $\mathbb{R}^N$ with critical terms ⋮ Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality ⋮ Multiple positive solutions for Schrödinger-Poisson system in $\mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent ⋮ On the multiplicity of non radial solutions for singular elliptic equations ⋮ Kirchhoff-Hardy fractional problems with lack of compactness ⋮ Sharp constants and optimizers for a class of Caffarelli-Kohn-Nirenberg inequalities ⋮ A nonhomogeneous fractional $p$-Kirchhoff type problem involving critical exponent in $\mathbb{R}^N$ ⋮ Solutions of a quasilinear elliptic problem involving a critical Sobolev exponent and multiple Hardy-type terms ⋮ The Webster scalar curvature problem on the three dimensional CR manifolds ⋮ Existence results for critical singular elliptic systems ⋮ Multiplicity result for a singular elliptic equation with indefinite nonlinearity ⋮ Large solutions for biharmonic maps in four dimensions ⋮ Problem with critical Sobolev exponent and with weight ⋮ Quasilinear elliptic problems involving multiple critical Hardy-Sobolev exponents ⋮ Positive solution to semilinear parabolic equation associated with critical Sobolev exponent ⋮ Extremal functions for singular Moser-Trudinger embeddings ⋮ On the existence and multiplicity of solutions for a class of singular elliptic problems ⋮ Remarks on GJMS operator of order six ⋮ Multiple positive solutions for semi-linear elliptic systems involving sign-changing weight on manifolds with conical singularities ⋮ Multiplicity of solutions for the noncooperative Schrödinger-Kirchhoff system involving the fractional $p$-Laplacian in ${\mathbb {R}}^N$ ⋮ Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem ⋮ Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity in $\mathbb{R}^3$ ⋮ Doubly critical problems involving fractional Laplacians in $\mathbb{R}^N$ ⋮ Local existence conditions for an equations involving the $p(x)$-Laplacian with critical exponent in $\mathbb R^N$ ⋮ Elliptic equations in dimension 2 with double exponential nonlinearities ⋮ Multiplicity of solutions to Kirchhoff type equations with critical Sobolev exponent ⋮ Existence of weak solutions to degenerate $p$-Laplacian equations and integral formulas ⋮ Multiplicity of concentrating positive solutions for Schrödinger-Poisson equations with critical growth ⋮ Existence results for Schrödinger $p(\cdot)$-Laplace equations involving critical growth in $\mathbb{R}^N$ ⋮ A Trudinger-Moser inequality for a conical metric in the unit ball ⋮ On a weak solution for a doubly critical fourth-order semilinear elliptic equation in a compact manifold ⋮ Existence of positive solutions for a class of \( p \& q$ elliptic problem with critical exponent and discontinuous nonlinearity ⋮ The Littlewood-Paley theory: a common thread of many works in nonlinear analysis ⋮ Critical quasilinear elliptic problems using concave-convex nonlinearities ⋮ A sharp Trudinger-Moser type inequality involving $L^n$ norm in the entire space $\mathbb{R}^n$ ⋮ Existence and nonexistence of ground state solutions to singular elliptic systems ⋮ Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group ⋮ Characterization of the Palais-Smale sequences for the conformal Dirac-Einstein problem and applications ⋮ A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities ⋮ Positive solutions for a quasilinear Schrödinger equation with critical growth ⋮ Parabolic H-measures ⋮ An improvement for the Trudinger-Moser inequality and applications ⋮ Multiple solutions for noncooperative $p(x)$-Laplacian equations in $\mathbb R^N$ involving the critical exponent ⋮ Ground state and multiple solutions via generalized Nehari manifold ⋮ Multiplicity of solutions for an elliptic problem with critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ The critical problem of Kirchhoff type elliptic equations in dimension four ⋮ Sharp asymptotics and compactness for local low energy solutions of critical elliptic systems in potential form ⋮ On the Neumann problem with the Hardy-Sobolev potential ⋮ On existence of mimimizers for the Hardy-Sobolev-Maz'ya inequality ⋮ On the nonhomogeneous Neumann problem with weight and with critical nonlinearity in the boundary ⋮ Semilinear subelliptic problems with critical growth on Carnot groups ⋮ Multiple solutions to singular critical elliptic equations ⋮ Singular elliptic problems in $\mathbb R^N$ with critical Sobolev-Hardy exponents ⋮ On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms ⋮ Nonvariational problems with critical growth ⋮ Interpolation inequalities between Sobolev and Morrey-Campanato spaces: a common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities ⋮ Critical points of the Trudinger-Moser trace functional with high energy levels ⋮ Existence of a nontrivial solution for a $(p,q)$-Laplacian equation with $p$-critical exponent in $\mathbb{R}^{N}$ ⋮ Symmetric solutions for singular quasilinear elliptic systems involving multiple critical Hardy-Sobolev exponents ⋮ Multiple solutions for the $p$-Laplacian problem with supercritical exponent ⋮ Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobolev and Hardy exponents ⋮ A class of Adams-Fontana type inequalities and related functionals on manifolds ⋮ Reverse Stein-Weiss inequalities on the upper half space and the existence of their extremals ⋮ On compactness of minimizing sequences subject to a linear differential constraint ⋮ Concentration-compactness principle for generalized Trudinger inequalities ⋮ Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations ⋮ A quasilinear elliptic equation with critical growth on compact Riemannian manifold ⋮ Multiplicity of semiclassical states for fractional Schrödinger equations with critical frequency ⋮ Near-extremizers of Young's inequality for Euclidean groups ⋮ Extremizability of Fourier restriction to the paraboloid ⋮ On the anisotropic Moser-Trudinger inequality for unbounded domains in $\mathbb{R}^n$ ⋮ Existence for $(p, q)$ critical systems in the Heisenberg group ⋮ Existence and concentration phenomena for a class of indefinite variational problems with critical growth ⋮ A note on strong-form stability for the Sobolev inequality ⋮ Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in ${{\mathbb{R}}}^N$ ⋮ Existence and concentration of positive solutions for $p$-fractional Schrödinger equations ⋮ Ground state solutions for fractional $p$-Kirchhoff equation with subcritical and critical exponential growth ⋮ Multiple solutions for a non-cooperative elliptic system of Kirchhoff type involving $p$-biharmonic operator and critical growth ⋮ Infinitely many solutions of Schrödinger-Poisson equations with critical and sublinear terms ⋮ Ground state solution and multiple solutions to elliptic equations with exponential growth and singular term ⋮ Existence and uniqueness of solutions for Choquard equation involving Hardy-Littlewood-Sobolev critical exponent ⋮ Hardy-Littlewood-Sobolev inequalities with the fractional Poisson kernel and their applications in PDEs ⋮ Ground state solutions for a semilinear elliptic problem with critical-subcritical growth ⋮ A class of semipositone $p$-Laplacian problems with a critical growth reaction term ⋮ $n$-Kirchhoff-Choquard equations with exponential nonlinearity ⋮ Two positive solutions for the Kirchhoff type elliptic problem with critical nonlinearity in high dimension ⋮ Multiplicity results for the biharmonic equation with singular nonlinearity of super exponential growth in $\mathbb{R}^4$ ⋮ Concentrating solutions for a magnetic Schrödinger equation with critical growth ⋮ Existence and concentration behavior of positive solutions for a quasilinear Schrödinger equation ⋮ Existence and concentration of solutions with compact support for elliptic problems with critical growth in $\mathbb R^N$ ⋮ A sharp inequality of Trudinger-Moser type and extremal functions in $H^{1, n}(\mathbb{R}^n)$ ⋮ On elliptic equations and systems with critical growth in dimension two ⋮ Multiplicity of solutions for quasilinear elliptic systems with singularity ⋮ On elliptic problems with two critical Hardy-Sobolev exponents at the same pole ⋮ Trudinger-Moser inequality on the whole plane with the exact growth condition ⋮ A quasilinear elliptic problem involving critical Sobolev exponents ⋮ Positive solutions for Kirchhoff-type equations with critical exponent in $\mathbb{R}^N$ ⋮ Moser-type trace inequalities for generalized Lorentz-Sobolev spaces ⋮ Fractional Sobolev-Hardy inequality in $\mathbb{R}^N$ ⋮ Systems of quasilinear elliptic equations involving multiple homogeneous nonlinearities ⋮ Moser-Trudinger inequality in grand Lebesgue space ⋮ Concentration-compactness principle for Moser-type inequalities in Lorentz-Sobolev spaces ⋮ PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT ⋮ HARDY-SOBOLEV INEQUALITY IN H¹(Ω) AND ITS APPLICATIONS ⋮ SYMMETRY BREAKING OF EXTREMAL FUNCTIONS FOR THE CAFFARELLI– KOHN–NIRENBERG INEQUALITIES ⋮ Singular perturbed Kirchhoff type problem with critical exponent ⋮ Trudinger-Moser inequalities in fractional Sobolev-Slobodeckij spaces and multiplicity of weak solutions to the fractional-Laplacian equation ⋮ Unnamed Item ⋮ The existence of positive solution for semilinear elliptic equations with multiple an inverse square potential and Hardy-Sobolev critical exponents ⋮ Existence and nondegeneracy of ground states in critical free boundary problems ⋮ Adams inequality with exact growth in the hyperbolic space ℍ4 and Lions lemma ⋮ Ground solutions for critical quasilinear elliptic equations via Pohožaev manifold method ⋮ Multiplicity of solutions for a nonlocal nonhomogeneous elliptic equation with critical exponential growth ⋮ On some multiple solutions for a $p(x)$-Laplacian equation with critical growth ⋮ Scattering for NLS with a delta potential ⋮ Concentration-compactness and extremal problems for a weighted Trudinger–Moser inequality ⋮ A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument ⋮ Q-Curvature on a Class of Manifolds with Dimension at Least 5 ⋮ Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent ⋮ Singular Moser–Trudinger inequality on simply connected domains ⋮ Trudinger–Moser inequality on the whole plane and extremal functions ⋮ On conformal invariants for elliptic systems with multiple critical exponents ⋮ Concentration compactness of Moser functionals on manifolds ⋮ Multiplicity of solutions for Kirchhoff type equations involving critical Sobolev exponents in high dimension ⋮ Solutions to nonlinear Neumann problems with an inverse square potential ⋮ Critical exponents, critical dimensions and the biharmonic operator ⋮ A Trudinger-Moser inequality in a weighted Sobolev space and applications ⋮ Improved Moser-Trudinger Inequality Involving L^p Norm in n Dimensions ⋮ Small linear perturbations of fractional Choquard equations with critical exponent ⋮ Energy asymptotics in the three-dimensional Brezis-Nirenberg problem ⋮ Curvature-driven wrinkling of thin elastic shells ⋮ Partially regular weak solutions of the Navier-Stokes equations in $\mathbb{R}^4 \times [0,\infty[$ ⋮ On nonexistence of extremals for the Trudinger-Moser functionals involving $L^p$ norms ⋮ Sharpened Trudinger-Moser inequalities on the Euclidean space and Heisenberg group ⋮ Concentration phenomena for fractional CR Yamabe type flows ⋮ Solutions to coupled critical elliptic systems involving attractive Hardy-type terms ⋮ On nonlocal Choquard system with Hardy-Littlewood-Sobolev critical exponents ⋮ Concentration-compactness principle for embedding into multiple exponential spaces on unbounded domains ⋮ Existence of solutions for Choquard type elliptic problems with doubly critical nonlinearities ⋮ Existence results for the conformal Dirac-Einstein system ⋮ Multiple solutions for a class of quasilinear Schrödinger-Poisson system in $\mathbb{R}^3$ with critical nonlinearity and zero mass ⋮ On the critical Choquard-Kirchhoff problem on the Heisenberg group ⋮ Fractional $(p, q)$-Schrödinger equations with critical and supercritical growth ⋮ Effect of lower order perturbation on maximization problem associated with Trudinger-Moser inequality ⋮ Lions-type properties for the $p$-Laplacian and applications to quasilinear elliptic equations ⋮ Asymptotic properties of critical points for subcritical Trudinger-Moser functional ⋮ The Benci-Cerami problem for the fractional Choquard equation with critical exponent ⋮ Existence results for fractional Brezis-Nirenberg type problems in unbounded domains ⋮ Nontrivial solutions for a $(p, q)$-type critical Choquard equation on the Heisenberg group ⋮ Maximization of Neumann eigenvalues ⋮ Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term ⋮ A nonhomogeneous Schrödinger equation involving nonlinearity with exponential critical growth and potential which can vanish at infinity ⋮ Fractional $p$-Laplacian problem with critical Stein-Weiss type term ⋮ Improved higher-order Sobolev inequalities on CR sphere ⋮ Existence and non-degeneracy of positive multi-bubbling solutions to critical elliptic systems of Hamiltonian type ⋮ A planar Schrödinger-Newton system with Trudinger-Moser critical growth ⋮ On Hamiltonian systems with critical Sobolev exponents ⋮ Generalized Chern-Simons-Schrödinger system with sign-changing steep potential well: critical and subcritical exponential case ⋮ Improved $L^p$-Folland-Stein-Sobolev inequality under constraints ⋮ Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent ⋮ High frequency approximation of solutions to Klein–Gordon equation in Orlicz framework ⋮ Semilinear elliptic equations for the fractional Laplacian involving critical exponential growth ⋮ On properness and related properties of quasilinear systems on unbounded domains ⋮ Multiple solutions to the Yamabe problem ⋮ Critical semilinear equations on the Heisenberg group ⋮ Solutions of the quasilinear elliptic problem with a critical Sobolev-Hardy exponent and a Hardy-type term ⋮ On the elliptic problems involving multi-singular inverse square potentials and critical Sobolev exponent ⋮ A surprising higher integrability property of mappings with positive determinant ⋮ A relation between the domain topology and the number of minimal nodal solutions for a quasilinear elliptic problem ⋮ The solvability of quasilinear Brezis-Nirenberg-type problems with singular weights ⋮ A mathematical programming problem with singular mixed pointwise-integral constraints ⋮ A compactness theorem of $n$-harmonic maps ⋮ Improved Sobolev inequalities on the Heisenberg group ⋮ On a fourth order elliptic equation with critical nonlinearity in dimension six ⋮ Solutions to critical elliptic equations with multi-singular inverse square potentials ⋮ Existence and properties of multiple positive solutions for semi-linear equations with critical exponents ⋮ Existence and asymptotic behavior of ground states for quasilinear singular equations involving Hardy-Sobolev exponents ⋮ Nonlinear Schrödinger equations with symmetric multi-polar potentials ⋮ A weighted form of Moser-Trudinger inequality on Riemannian surface ⋮ Multiple solutions of a nonlinear elliptic equation involving Neumann conditions and a critical Sobolev exponent. ⋮ Nonlinear biharmonic equations with critical potential ⋮ Some existence results for the Webster scalar curvature problem in presence of symmetry ⋮ Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces ⋮ A generalization of an extensible beam equation with critical growth in $\mathbb{R}^N$ ⋮ Concentration analysis in Banach spaces ⋮ Critical points for a functional involving critical growth of Trudinger-Moser type ⋮ Positive solutions of elliptic problems involving both critical Sobolev nonlinearities on exterior regions ⋮ The group classification of Lane-Emden systems ⋮ High-Frequency Dynamics for the Schrödinger Equation, with Applications to Dispersion and Observability ⋮ Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero ⋮ A compactness result for polyharmonic maps in the critical dimension ⋮ On a class of singular Trudinger-Moser type inequalities and its applications ⋮ Multiplicity of solutions to the weighted critical quasilinear problems ⋮ On the Hénon equation: asymptotic profile of ground states. II ⋮ A note about the generalized Hardy-Sobolev inequality with potential in $L^{p,d}(\mathbb R^n)$ ⋮ Existence and multiplicity of solutions for a class ofp&qelliptic problems with critical exponent ⋮ Hardy-Sobolev type inequalities on the H-type group ⋮ Existence and nonexistence results for critical growth polyharmonic elliptic systems ⋮ Binding of atoms and stability of molecules in hartree and thomas-fermi type theories. ⋮ Sign-changing and symmetry-breaking solutions to singular problems ⋮ Asymptotic Estimates for the Parabolic-Elliptic Keller-Segel Model in the Plane ⋮ Characterization of the lack of compactness of $H^2_{\rm rad}({\mathbb R}^4)$ into the Orlicz space ⋮ On a p⋅-biharmonic problem of Kirchhoff type involving critical growth ⋮ On an inequality by N. Trudinger and J. Moser and related elliptic equations ⋮ H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations ⋮ Sharp local isoperimetric inequalities involving the scalar curvature ⋮ Multiple positive solutions for semilinear elliptic equations in ℝ involving critical exponents ⋮ Singular elliptic equations with nonlinearities of subcritical and critical growth ⋮ A global compactness result for singular elliptic problems involving critical Sobolev exponent ⋮ Multiple solutions for a quasilinear Schrödinger equation involving critical Hardy–Sobolev exponent with Robin boundary condition ⋮ Relative category and multiplicity of positive solutions for the equation ⋮ Positive solutions of certain elliptic equations involving critical Sobolev exponents ⋮ Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces ⋮ Stability results for some nonlinear elliptic equations involving thep-Laplacian with critical Sobolev growth ⋮ Unnamed Item ⋮ Limiting Aspects of Nonconvex ${TV}^{\phi}$ Models ⋮ SOME REMARKS ON THE EQUATION FOR VARYING λ,pAND VARYING DOMAINS* ⋮ Positive solution for neumann problem with critical non linearity on boundary ⋮ Semilinear elliptic problems with singular potentials in ℝ^N ⋮ Adams Type Inequality and Application for a Class of Polyharmonic Equations with Critical Growth ⋮ On existence of solution of variational multivalued elliptic equations with critical growth via the Ekeland principle ⋮ About the behavior of regular Navier-Stokes solutions near the blow up ⋮ A sharp Trudinger-Moser type inequality in $\mathbb {R}^2$ ⋮ On a p(x)-Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument ⋮ On the stability of global solutions to the three-dimensional Navier-Stokes equations ⋮ Schrödinger-Poisson equations in R^3 involving critical Sobolev exponents ⋮ Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold ⋮ Existence and multiplicity results in the presence of symmetry for elliptic equations with critical Sobolev exponent ⋮ Existence and multiplicity of homoclinic orbits for potentials on unbounded domains ⋮ Unnamed Item ⋮ Eigenvalue problems for quasilinear elliptic systems with limiting nonlinearity ⋮ Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds ⋮ Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities ⋮ Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ ⋮ A minimization problem on RN involving critical Sobolev exponent ⋮ EXISTENCE OF POSITIVE SOLUTION FOR INDEFINITE KIRCHHOFF EQUATION IN EXTERIOR DOMAINS WITH SUBCRITICAL OR CRITICAL GROWTH ⋮ On Limits Of Solutions Of Elliptic Problems With Nearly Critical Exponent ⋮ Unnamed Item ⋮ Vanishing-concentration-compactness alternative for the Trudinger–Moser inequality in ℝN ⋮ Very singular problems with critical nonlinearities in two dimensions ⋮ Existence and boundedness of a minimiser for a constrained minimisation problem on Rⁿ with limiting exponent ⋮ Multiple finite energy states for critical potential systems ⋮ Extrema problems with critical sobolev exponents on unbounded domains ⋮ Symmetry properties in higher order semilinear elliptic equations ⋮ Uniqueness for semilinear polyharmonic problems ⋮ Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature ⋮ A free boundary approach to the Faber-Krahn inequality ⋮ On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain ⋮ Nonlinear profile decomposition and the concentration phenomenon for supercritical generalized KDV equations ⋮ On diperna-majda concentration sets for two-dimensional incompressible flow ⋮ On the existence of multiple positive solutions of critical semilinear elliptic problems ⋮ On semilinear Neumann problems with critical growth for the n-Laplacian ⋮ An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds ⋮ Ground state solutions of Hamiltonian elliptic systems in dimension two ⋮ Asymptotic behaviour of ground states ⋮ On extremals for the Trudinger-Moser inequality with vanishing weight in the N-dimensional unit ball ⋮ On generalized Moser-Trudinger inequalities without boundary condition ⋮ A Trudinger-Moser type inequality and its extremal functions in dimension two ⋮ Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponents ⋮ EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH ⋮ Strongly indefinite systems with critical Sobolev exponents ⋮ Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains ⋮ GROUP INVARIANCE AND POHOZAEV IDENTITY IN MOSER-TYPE INEQUALITIES ⋮ Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory ⋮ On some nonlinear equations involving the_p-laplacian with critical sobolev growth and perturbation terms ⋮ Critical growth problems for polyharmonic operators ⋮ Stability properties for solitary waves in 3 space dimensions ⋮ Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four ⋮ Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces ⋮ Positive Solutions of Semilinear Equations in Cones ⋮ Uniqueness of positive solutions for singular problems involving the $p$-Laplacian ⋮ A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface ⋮ On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent ⋮ On Limits Of Solutions of Quasilinear Equations With Nearly Critical Exponents ⋮ The effect of a discontinuous weight for a critical Sobolev problem ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:4257011 Asymptotic and limiting profiles of blowup solutions of the nonlinear Schr�dinger equation with critical power] ⋮ Cocompact Imbeddings and Structure of Weakly Convergent Sequences ⋮ Classification of positive solutions to the critical fractional Choquard equation in ⋮ Existence and multiplicity of solutions for a Kirchhoff system with critical growth ⋮ Singular limit of quasilinear Neumann problems ⋮ EXISTENCE OF SOLUTIONS FOR CRITICAL SYSTEMS WITH VARIABLE EXPONENTS ⋮ Entire nodal solutions to the critical Lane-Emden system ⋮ General sharp weighted Caffarelli–Kohn–Nirenberg inequalities ⋮ EXISTENCE OF POSITIVE SOLUTION FOR A QUASI-LINEAR PROBLEM WITH CRITICAL GROWTH IN ^N₊ ⋮ Nonlinear elliptic problem related to the Hardy inequality with singular term at the boundary ⋮ Unnamed Item ⋮ Sign-changing multi-bump solutions for nonlinear Schrödinger equations with steep potential wells ⋮ Strongly interacting bumps for the Schrödinger–Newton equations ⋮ Unnamed Item ⋮ Two dimensional elliptic equation with critical nonlinear growth ⋮ A Palais-Smale approach to problems in Esteban-Lions domains with holes ⋮ Estimations of the best constant involving the L²norm in Wente's inequality and compact H-surfaces in Euclidean space ⋮ Double logarithmic inequality with a sharp constant ⋮ Improved Adams-type inequalities and their extremals in dimension 2m ⋮ Existence and multiplicity of positive solutions for a critical weight elliptic system in ℝN ⋮ Sobolev Inequalities for Weighted Gradients ⋮ Soliton Like Solutions of a Lorentz Invariant Equation in Dimension 3 ⋮ Solutions for the fractional p-Laplacian systems with several critical Sobolev-Hardy terms ⋮ Schrödinger p⋅–Laplace equations in RN involving indefinite weights and critical growth ⋮ Periodic minimizers of a ternary non-local isoperimetric problem ⋮ On a class of Kirchhoff problems via local mountain pass ⋮ Soliton solutions for quasilinear Schrödinger equations, I ⋮ Integral equations on compact manifold with boundary ⋮ Singular Trudinger–Moser inequality with L^p norm and the existence of extremals ⋮ Multiplicity results for nonlocal critical problems involving Hardy potential in the whole space ⋮ The semilinear elliptic equations with double weighted critical exponents ⋮ Existence of extremizers for Fourier restriction to the moment curve ⋮ Sharp constant in a Sobolev inequality ⋮ On a variational problem proposed by H. Brézis ⋮ Sign-changing solutions for modified Schrödinger–Poisson system with general nonlinearity ⋮ Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity ⋮ Nonlinear Schrödinger equations involving exponential critical growth with unbounded or vanishing potentials ⋮ Morse inequalities at infinity for a resonant mean field equation ⋮ Weighted Sobolev-type embedding theorems for functions with symmetries ⋮ Infinitely many solutions to elliptic systems involving critical exponents and Hardy potential ⋮ EXISTENCE AND BIFURCATION RESULTS FOR FOURTH-ORDER ELLIPTIC EQUATIONS INVOLVING TWO CRITICAL SOBOLEV EXPONENTS ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ On a nonhomogeneous Kirchhoff-type elliptic problem with critical exponential in dimension two ⋮ Existence and multiplicity results for critical anisotropic Kirchhoff-type problems with nonlocal nonlinearities ⋮ On an open question of Ricceri concerning a Kirchhoff-type problem ⋮ Symmetric solutions for a 2D critical Dirac equation ⋮ The nonexistence of extremals for the Hardy-Trudinger-Moser inequality in the hyperbolic space ⋮ Existence of positive solutions for a class of Kirchhoff type systems involving critical exponents ⋮ Multiple solutions for singularly perturbed nonlinear magnetic Schrödinger equations ⋮ Multiplicity of positive solutions to a critical fractional equation with Hardy potential and concave–convex nonlinearities ⋮ Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions ⋮ A new class of traveling solitons for cubic fractional nonlinear Schrödinger equations ⋮ Ground state solution for a class of Schrödinger equations involving general critical growth term ⋮ On some weighted fourth-order equations ⋮ Multiplicity and concentration of solutions for a fractional $p$-Kirchhoff type equation ⋮ Existence of solutions for critical (p,q)-Laplacian equations in ℝN ⋮ Infinitely many solutions for Schrödinger–Newton equations ⋮ A singular Liouville equation on two-dimensional domains ⋮ Sub-elliptic problems with multiple critical Sobolev-Hardy exponents on Carnot groups ⋮ Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity ⋮ Positive solutions for a class semipositone quasilinear problem with Orlicz–Sobolev critical growth ⋮ 𝑊^{1,𝑝} approximation of the Moser–Trudinger inequality ⋮ An existence result for a fractional critical $(p, q)$-Laplacian problem with discontinuous nonlinearity ⋮ Hardy–Littlewood–Sobolev inequality and existence of the extremal functions with extended kernel ⋮ Multiplicity of solutions for the noncooperative Choquard-Kirchhoff system involving Hardy-Littlewood-Sobolev critical exponent on the Heisenberg group ⋮ Nontrivial solutions for the polyharmonic problem: existence, multiplicity and uniqueness ⋮ Multiplicity results for double phase problems involving a new type of critical growth ⋮ Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy–Sobolev–Maz’ya terms ⋮ Concentration-compactness results for systems in the Heisenberg group ⋮ Unnamed Item ⋮ The Lane-Emden equation with variable double-phase and multiple regime ⋮ MINIMIZERS FOR THE EMBEDDING OF BESOV SPACES ⋮ Unnamed Item ⋮ Stationary Kirchhoff equations involving critical growth and vanishing potential ⋮ The effect of curvature in fractional Hardy–Sobolev inequality involving the spectral Dirichlet Laplacian ⋮ Concentration-compactness principle of singular Trudinger–Moser inequality involving N-Finsler–Laplacian operator ⋮ A critical fractional Choquard–Kirchhoff problem with magnetic field ⋮ ON A CLASS OF NONCOOPERATIVE FOURTH-ORDER ELLIPTIC SYSTEMS WITH NONLOCAL TERMS AND CRITICAL GROWTH ⋮ Ground state and non-ground state solutions of some strongly coupled elliptic systems ⋮ Unnamed Item ⋮ Non-degeneracy for the critical Lane–Emden system ⋮ Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space ⋮ Lack of compactness in the 2D critical Sobolev embedding, the general case ⋮ A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient ⋮ Unnamed Item ⋮ Kirchhoff–Schrödinger equations in ℝ2 with critical exponential growth and indefinite potential ⋮ A critical Kirchhoff‐type problem involving the ‐Laplacian ⋮ Multiplicity of concentrating positive solutions for nonlinear Kirchhoff type problems with critical growth ⋮ First Bloch eigenvalue in high contrast media ⋮ Homoclinic orbits for a class of Hamiltonian systems ⋮ Existence and multiplicity results for singular quasilinear elliptic equation on unbounded domain ⋮ Multiple positive solutions of nonhomogeneous equations involving the $p$-Laplacian ⋮ Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $\mathbb{R}^N$ ⋮ Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials ⋮ Critical and noncritical regions on the critical hyperbola ⋮ Unnamed Item ⋮ Nontrivial solutions for a class of semilinear biharmonic problems involving critical exponents ⋮ The scalar curvature equation on $\mathbb R^N$ ⋮ On perturbations of a class of a periodic $m$-Laplacian equation with critical growth ⋮ Critical semilinear equations on the Heisenberg group: the effect of the topology of the domain ⋮ Diagonal Compactness for Critical Elliptic Systems in Potential Form ⋮ Structure theorems for 2D linear and nonlinear Schrödinger equations ⋮ Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions ⋮ Existence results for the $p$-Laplacian with nonlinear boundary conditions ⋮ Lower semicontinuity of functionals via the concentration-compactness principle ⋮ On the Caffarelli-Kohn-Niremberg type inequalities and related topics ⋮ Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials ⋮ Multiple solutions for weighted nonlinear elliptic system involving critical exponents ⋮ Infinitely many solutions for non-local elliptic non-degeneratep-Kirchhoff equations with critical exponent ⋮ Existence of infinitely many homoclinic orbits in Hamiltonian systems ⋮ Existence of solutions for critical Choquard equations via the concentration-compactness method ⋮ Existence of positive solution for the nonlinear Kirchhoff type equations in the half space with a hole ⋮ Asymptotics for optimizers of the fractional Hardy–Sobolev inequality ⋮ Quasilinear Scalar Field Equations Involving Critical Sobolev Exponents and Potentials Vanishing at Infinity ⋮ On a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents ⋮ Below-threshold solutions of a focusing energy-critical heat equation in ℝ⁴ ⋮ Decay estimates and symmetry of finite energy solutions to elliptic systems in \mathbb{R}^n ⋮ Adams' Inequality with the Exact Growth Condition in ℝ⁴ ⋮ Extremal functions for the modified Trudinger-Moser inequalities in two dimensions ⋮ Existence and symmetry of positive ground states for a doubly critical Schrödinger system ⋮ Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations ⋮ A variational method for solving quasilinear elliptic systems involving symmetric multi-polar potentials ⋮ INFINITELY MANY SOLUTIONS FOR A ZERO MASS SCHRÖDINGER-POISSON-SLATER PROBLEM WITH CRITICAL GROWTH ⋮ Existence of multiple solutions for quasilinear elliptic equation with critical Sobolev–Hardy terms ⋮ On Kirchhoff type problems involving critical and singular nonlinearities ⋮ Existence of critical points for noncoercive functionals with critical Sobolev exponent

This page was built for publication: The concentration-compactness principle in the calculus of variations. The limit case. I