A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
From MaRDI portal
Publication:1392744
DOI10.1007/s000140050052zbMath0933.35057OpenAlexW2107614808MaRDI QIDQ1392744
Publication date: 15 March 2000
Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s000140050052
Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60) Solutions to PDEs in closed form (35C05)
Related Items
PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT, Qualitative properties for solutions to subcritical fourth order systems*, Integrability of positive solutions of the integral system involving the Riesz potentials, On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents, Semilinear Elliptic Equation with Biharmonic Operator and Multiple Critical Nonlinearities, Infinitely many peak solutions for a biharmonic equation involving critical exponent, Local and Nonlocal Singular Liouville Equations in Euclidean Spaces, Isolated singularities of polyharmonic operator in even dimension, Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold, Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds, Monotonicity and symmetry of positive solutions to fractional p-Laplacian equation, On some weighted fourth-order equations, Liouville-type theorems for higher-order Lane–Emden system in exterior domains, Liouville theorem for Hénon-Hardy systems in the unit ball, Positive solutions for biharmonic equations: existence, uniqueness and multiplicity, Classification of solutions for some mixed order elliptic system, Nontrivial solutions for the polyharmonic problem: existence, multiplicity and uniqueness, On a biharmonic elliptic problem with slightly subcritical non-power nonlinearity, Simple blow-up solutions of singular Liouville equations, Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres, Liouville type theorems for the generalized higher order Choquard-Pekar equation, Existence and asymptotic behavior of non-normal conformal metrics on ℝ4 with sign-changing Q-curvature, Classical solutions to a Hartree type system, Classification of solutions for mixed order conformally system with Hartree-type nonlinearity in ℝn, Q-curvature type problem on bounded domains of R n, Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity, Qualitative properties for solutions to conformally invariant fourth order critical systems, Liouville type theorems for poly-harmonic Dirichlet problems of Hénon-Hardy type equations on a half space or a ball, Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space, Improved Beckner's inequality for axially symmetric functions on \(\mathbb{S}^4\), Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity, Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application, Asymptotic behavior and classification of solutions to Hartree type equations with exponential nonlinearity, Concentrating solutions for a biharmonic problem with supercritical growth, Classification of solutions to several semi-linear polyharmonic equations and fractional equations, Singular metrics of constant negative \(Q\)-curvature in Euclidean spaces, Nonradial singular metrics of constant \(Q\)-curvature, Asymptotic behavior of least energy nodal solutions for biharmonic Lane-Emden problems in dimension four, Classification of Solutions to Mixed Order Elliptic System with General Nonlinearity, Singular limit solutions for a four‐dimensional semilinear elliptic Kuramoto–Sivashinsky system in some general case, Positive solutions of biharmonic elliptic problems with a parameter, The prescribed \(Q\)-curvature flow for arbitrary even dimension in a critical case, Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation, Liouville-Type Theorems for Nonlinear Elliptic and Parabolic Problems, Unnamed Item, Liouville theorems for stable at infinity solutions of Lane–Emden system, A Liouville-type theorem for higher order elliptic systems, A Liouville-type theorem for higher order elliptic systems, Unnamed Item, Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics, Unnamed Item, Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth, Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension, On a class of semilinear elliptic systems and applications in polyharmonic equations, ON THE HIGHER ORDER CONFORMAL COVARIANT OPERATORS ON THE SPHERE, Classification of Solutions of a Conformally Invariant Third Order Equation in ℝ3, A Liouville type theorem for non-linear elliptic systems involving advection terms, Conformal metrics in \(\mathbb {R}^{2m}\) with constant \(Q\)-curvature and arbitrary volume, Liouville Type Theorems for Positive Solutions of Elliptic System in ℝN, Radial symmetry of non-maximal entire solutions of a bi-harmonic equation with exponential nonlinearity, Some nonexistence theorems for semilinear fourth-order equations, COMPACTNESS AND GLOBAL ESTIMATES FOR A FOURTH ORDER EQUATION OF CRITICAL SOBOLEV GROWTH ARISING FROM CONFORMAL GEOMETRY, Compactness of solutions to some geometric fourth-order equations, Unnamed Item, Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians, Symmetry and non-existence of positive solutions for PDE system with Navier boundary conditions on a half space, Infinitely Many Spiky Solutions for a Hénon Type Biharmonic Equation with Critical Growth, Improved Adams-type inequalities and their extremals in dimension 2m, Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations, Concentration Phenomena in a Biharmonic Equation Involving the Critical Sobolev Exponent, Liouville theorems for fractional and higher-order Hénon–Hardy systems on ℝn, Constant 𝑄-curvature metrics with a singularity, Prescribing \(Q\)-curvature on higher dimensional spheres, Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications, Normal conformal metrics on \(\mathbb{R}^4\) with \(Q\)-curvature having power-like growth, The fourth order elliptic problem with exponential nonlinearity, Existence of infinitely many spike solutions for a critical Hénon type biharmonic equation, Symmetry of positive solutions of fractional Laplacian equation and system with Hardy-Sobolev exponent on the unit ball, Oscillatory radial solutions for subcritical biharmonic equations, Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent, Critical points at infinity in a fourth order elliptic problem with limiting exponent, Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\), Qualitative properties and standard estimates of solutions for some fourth-order elliptic systems, Profile of bubbling solutions to a Liouville system, Classification theorems for solutions of higher order boundary conformally invariant problems. I., Concentration phenomena for a fourth-order equation with exponential growth: the radial case, Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity, A Liouville type theorem for polyharmonic elliptic systems, Symmetry and nonexistence of positive solutions for fractional systems, The Paneitz curvature problem on lower-dimensional spheres, Classification of extremal functions to logarithmic Hardy-Littlewood-Sobolev inequality on the upper half space, Existence of conformal metrics with prescribed Q-curvature, The nonlocal Liouville-type equation in \(\mathbb {R}\) and conformal immersions of the disk with boundary singularities, Fast decay estimates for integrable solutions of the Lane-Emden type integral systems involving the Wolff potentials, Non-compactness of the prescribed \(Q\)-curvature problem in large dimensions, A Liouville type theorem for poly-harmonic Dirichlet problems in a half space, A radial symmetry and Liouville theorem for systems involving fractional Laplacian, Prescribed \(Q\)-curvature flow on \(S^n\), Radial solutions of a polyharmonic equation with power nonlinearity, Symmetry of solutions for a fractional system, Topological degree for solutions of fourth order mean field equations, Liouville-type theorems for semilinear elliptic systems, Classification of nonnegative classical solutions to third-order equations, A classification result for the quasi-linear Liouville equation, Sharp Sobolev inequalities of second order, Qualitative behavior of global solutions to some nonlinear fourth order differential equations, A note on the existence of positive solutions for a fourth-order semilinear elliptic system, Existence and concentration of positive solutions for a super-critical fourth order equation, The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\), Qualitative properties and standard estimates of solutions for some fourth order elliptic equations, Compactness of conformal metrics with constant \(Q\)-curvature. I, Nonradial solutions for a conformally invariant fourth order equation in \(\mathbb {R}^4\), Existence and stability of entire solutions to a semilinear fourth order elliptic problem, Regularity and classification of solutions to static Hartree equations involving fractional Laplacians, Conformal metrics on \(\mathbb{R}^{2m}\) with constant \(Q\)-curvature, prescribed volume and asymptotic behavior, Uniqueness and asymptotic behavior of solutions of a biharmonic equation with supercritical exponent, A note on minimizing the Moser--Trudinger functional of high order derivatives, Fractional Adams-Moser-Trudinger type inequalities, Nonexistence of solutions to singular Q-curvature equations, Liouville type results for semilinear biharmonic problems in exterior domains, Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians, Uniform bounds for higher-order semilinear problems in conformal dimension, The Paneitz equation in hyperbolic space, On the existence for an integral system including \(m\) equations, Priori estimates and asymptotic properties of solutions for some fractional order elliptic equations, On the sixth-order Joseph-Lundgren exponent, Proof of the Hénon-Lane-Emden conjecture in \(\mathbb{R}^3\), Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes, Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order, Conformally Euclidean metrics on \(\mathbb{R}^n\) with arbitrary total Q-curvature, Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation, Liouville results for elliptic equations in strips with finite Morse index, Asymptotic expansion of radial solutions for supercritical biharmonic equations, Q-curvature flow with indefinite nonlinearity, Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space, A classification of positive solutions of some integral systems, Conformal metrics with prescribed \(Q\)-curvature on \(S^{n}\), The prescribed boundary mean curvature problem on \(\mathbb B^4\), Exact solutions of nonlinear conformally invariant integral equations in \(\mathbf R^3\), Remark on some conformally invariant integral equations: the method of moving spheres, Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three, Some existence results for a paneitz type problem via the theory of critical points at infinity, On the prescribed \(Q\)-curvature problem on \(S^n\), Uniqueness and non-existence theorems for conformally invariant equations, Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities, A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\), Adams' inequalities for bi-Laplacian and extremal functions in dimension four, A Liouville-type result for a fourth order equation in conformal geometry, A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems, Constant \(Q\)-curvature metrics near the hyperbolic metric, Direct methods for pseudo-relativistic Schrödinger operators, Method of scaling spheres for integral and polyharmonic systems, Positive supersolutions of fourth-order nonlinear elliptic equations: explicit estimates and Liouville theorems, Local behavior of positive solutions of higher order conformally invariant equations with a singular set, Symmetric properties for Choquard equations involving fully nonlinear nonlocal operators, Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds, The proof of the Lane-Emden conjecture in four space dimensions, Singular solutions of the Liouville equation in a punctured disc, Liouville theorems for nonnegative solutions to Hardy-Hénon type system on a half space, Classification of positive radial solutions to a weighted biharmonic equation, A Liouville-type theorem for an integral equation on a half-space \(\mathbb R_+^n\), On the Chern-Gauss-Bonnet integral for conformal metrics on \(\mathbb{R}^4\), Nonexistence and radial symmetry of positive solutions of semilinear elliptic systems, Concentration phenomena to a higher order Liouville equation, Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities, A threshold phenomenon for embeddings of \({H^m_0}\) into Orlicz spaces, On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent, Existence and stability properties of entire solutions to the polyharmonic equation \((-\Delta)^{m}u=e^{u}\) for any \(m\geq 1\), Sharp criteria of Liouville type for some nonlinear systems, Nonexistence of positive solutions for polyharmonic systems in \(\mathbb{R}^N_+\), A Liouville-type theorem for higher order elliptic systems of Hénon-Lane-Emden type, Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents, Constant \(Q\)-curvature metrics on conic 4-manifolds, Liouville type theorem for nonlinear elliptic system involving Grushin operator, Classification of solutions to mixed order conformally invariant systems in \({\mathbb{R}}^2\), Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell system involving the fractional Laplacian, Liouville-type theorem for high order degenerate Lane-Emden system, Single-point condensation phenomena for a four-dimensional biharmonic Ren-Wei problem, Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in \(\mathbb{R}^2\) and \(\mathbb{R}^3\), Asymptotic expansions for singular solutions of conformal Q-curvature equations, Normal conformal metrics on \(\mathbb{R}^4\) with singular \(Q\)-curvature having power-like growth, Blow up solutions for a 4-dimensional Emden-Fowler system of Liouville type, Nonlinear biharmonic equations with negative exponents, Classification of nonnegative solutions to fractional Schrödinger-Hatree-Maxwell type system, Classification of solutions for some elliptic system, Existence and non-existence results for the higher order Hardy-Hénon equations revisited, Quantization for a fourth order equation with critical exponential growth, Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay, Classification of solutions to higher fractional order systems, Existence and non-existence of extremals for critical Adams inequality in any even dimension, Liouville theorems for stable solutions of biharmonic problem, Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane-Emden-Hardy equations, Classification and a priori estimates for the singular prescribing \(Q\)-curvature equation on 4-manifold, Large singular solutions for conformal \(Q\)-curvature equations on \(\mathbb{S}^n\), Classification of solutions to a system of \(n^{\mathrm{th}}\) order equations on \(\mathbb{R}^n\), Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications, Singular limit solutions for a 4-dimensional semilinear elliptic system of Liouville type, On Delaunay solutions of a biharmonic elliptic equation with critical exponent, ``Large conformal metrics of prescribed \(Q\)-curvature in the negative case, The Paneitz curvature problem on \(S^n\), Radial singular solutions for a fourth order equation with negative exponents, Existence and nonexistence of extremals for critical Adams inequalities in \(\mathbb{R}^4\) and Trudinger-Moser inequalities in \(\mathbb{R}^2\), The \(\operatorname{SU}(3)\) Toda system with multiple singular sources, Classification to the positive radial solutions with weighted biharmonic equation, Liouville type theorems for elliptic equations with Dirichlet conditions in exterior domains, Positive solutions for a class of biharmonic problems: existence, nonexistence and multiplicity, Liouville theorem for poly-harmonic functions on \(\mathbb{R}^n_+ \), Liouville type theorem for higher order Hénon equations on a half space, Classification of positive solutions for an integral system on the half space, On the perturbed \(Q\)-curvature problem on \(\mathbb S^4\), The Gel'fand problem for the biharmonic operator, Further study of entire radial solutions of a biharmonic equation with exponential nonlinearity, Liouville type theorems, a priori estimates and existence of solutions for critical and super-critical order Hardy-Hénon type equations in \(\mathbb{R}^n\), Super poly-harmonic property of solutions for Navier boundary problems on a half space, Existence results for Liouville equations and systems, Maximum principles and monotonicity of solutions for fractional \(p\)-equations in unbounded domains, On the Hénon-Lane-Emden conjecture, Local estimates for conformal \(Q\)-curvature equations, Gelfand problem and hemisphere rigidity, Remarks on Entire Solutions for Two Fourth-Order Elliptic Problems, Solutions of Liouville equations with non-trivial profile in dimensions 2 and 4, Conformal metrics on \(\mathbb R^{2m}\) with constant \(Q\)-curvature and large volume, Non-stability of Paneitz-Branson type equations in arbitrary dimensions, Asymptotic behavior of solutions for some elliptic equations in exterior domains, Liouville theorems for nonnegative solutions to static weighted Schrödinger-Hartree-Maxwell type equations with combined nonlinearities, On finite Morse index solutions of higher order fractional elliptic equations, Constant \(Q\)-curvature metrics in arbitrary dimension, Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction, Infinitely many sign-changing solutions to a conformally invariant integral equation on \(\mathbb{R}^n\), Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities, A Paneitz-Branson type equation with Neumann boundary conditions, QUANTIZATION FOR THE PRESCRIBED Q-CURVATURE EQUATION ON OPEN DOMAINS, A Liouville theorem for high order degenerate elliptic equations, Nonexistence of positive solutions for an integral equation related to the Hardy-Sobolev inequality, Radial symmetry of entire solutions of a bi-harmonic equation with exponential nonlinearity, Radial entire solutions for supercritical biharmonic equations, Single blow-up solutions for a slightly subcritical biharmonic equation, Concentration and multiplicity of solutions for a fourth-order equation with critical nonlinearity, On a fourth order elliptic equation with critical nonlinearity in dimension six, Best constants and minimizers for embeddings of second order Sobolev spaces, Liouville-type theorems for polyharmonic systems in \(\mathbb R^N\), Concentration phenomena for Liouville's equation in dimension four, Convergence of the \(Q\)-curvature flow on \(S^{4}\), Symmetry and classification of solutions to an integral equation of the Choquard type, Fast cubature of high dimensional biharmonic potential based on approximate approximations, Critical regularity for elliptic equations from Littlewood-Paley theory, Exact multiplicity for the perturbed Q-curvature problem in \(\mathbb{R}^N, N \geq 5\), A subcritical approximation of the Paneitz problem on spheres, On a critical fourth order PDE with Navier boundary condition, A degree theory framework for semilinear elliptic systems, A compactness theorem on Branson's \(Q\)-curvature equation, Bôcher-type results for the fourth and higher order equations on singular manifolds with conical metrics, Radial symmetry of entire solutions of a biharmonic equation with supercritical exponent, Monotonicity formulas for coupled elliptic gradient systems with applications, Improved Beckner's inequality for axially symmetric functions on \(\mathbb{S}^n\), Classification of nonnegative solutions to static Schrödinger-Hartree and Schrödinger-Maxwell Equations with combined nonlinearities, Higher order conformally invariant equations in \( \mathbb{R}^3 \) with prescribed volume, Nonexistence of positive solutions to \(n\)-th order equations in \(\mathbb{R}^n\), Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on \(\mathbb{S}^n\), Uniqueness for the nonlocal Liouville equation in \(\mathbb{R}\), Non-radial solutions to a bi-harmonic equation with negative exponent, The effect of pinching conditions in prescribing \(Q\)-curvature on standard spheres, Optimal Liouville-type theorems for polyharmonic elliptic gradient systems and applications, Some weighted fourth-order Hardy-Hénon equations, New types of Caffarelli-Kohn-Nirenberg inequalities and applications, Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents, Blow-up in coupled solutions for a \(4\)-dimensional semilinear elliptic Kuramoto-Sivashinsky system, Classification of nonnegative solutions to Schrödinger equation with logarithmic nonlinearity, Liouville theorems for fractional Hénon equation and system on \(\mathbb{R}^n\), Deformations of \(Q\)-curvature. II., SOME REMARKS ON THE CURVATURE TYPE PROBLEM ON, Infinitely many sign-changing solutions of a critical fractional equation
