On an Elliptic Equation with Concave and Convex Nonlinearities

DOI10.2307/2161107zbMath0848.35039OpenAlexW4255203103MaRDI QIDQ4874216

Publication date: 27 October 1996

Full work available at URL: https://doi.org/10.2307/2161107

Hamiltonian systems elliptic equations concave nonlinearities symmetrie Mountain-Pass Theorem

Nonlinear boundary value problems for linear elliptic equations (35J65) Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items

Positive solutions of certain elliptic equations involving critical Sobolev exponents, Multiplicity of solutions for critical singular problems, A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence, Competition phenomena for elliptic equations involving a general operator in divergence form, Nodal solutions for Schrödinger-Poisson systems with concave-convex nonlinearities, The Unique Continuation Property of Sublinear Equations, An improved Fountain theorem and its application, Paths to uniqueness of critical points and applications to partial differential equations, Multiplicity of positive solutions to a critical fractional equation with Hardy potential and concave–convex nonlinearities, Multiplicity results for a non-local problem with concave and convex nonlinearities, On concave perturbations of a periodic elliptic problem in R2 involving critical exponential growth, Infinitely many positive energy solutions for an elliptic equation involving critical Sobolev growth, Hardy potential and concave-convex nonlinearity, Infinitely many solutions for a double critical Sobolev problem with concave nonlinearities, Existence of non-negative solutions for a system with concave-convex nonlinearity, Unnamed Item, Two disjoint and Infinite sets of solutions for a nonlocal problem involving a Hardy potential and critical growth with concave nonlinearities, Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent, Quasilinear Schrödinger equations with concave and convex nonlinearities, Existence of infinitely many solutions of nonlinear Steklov-Neumann problem, Existence and multiplicity of positive solutions to sub-elliptic systems with multiple critical exponents on Carnot groups, Two disjoint and infinite sets of solutions for an elliptic equation involving critical Hardy-Sobolev exponents, Multiple solutions for discrete Schrödinger equations with concave-convex nonlinearities, Elliptic equations with critical and supercritical growth at the boundary, Infinitely many rotating periodic solutions for second-order Hamiltonian systems, Infinitely many solutions for an elliptic equation in divergent form with critical Sobolev exponent and concave-convex nonlinearity, A class of Schrödinger elliptic equations involving supercritical exponential growth, Multiple positive solutions of Kirchhoff-type equations with concave terms, Two disjoint and infinite sets of solutions for an elliptic equation with critical Hardy-Sobolev-Maz'ya term and concave-convex nonlinearities, On a Hamiltonian elliptic system with concave and convex nonlinearities, Existence of infinitely many solutions to semilinear elliptic Neumann problems with concave-convex type nonlinearity, Multiple existence of non-radial solutions with group invariance for sublinear elliptic equations, Zero energy critical points of functionals depending on a parameter., Infinitely many regular weak solutions for odd symmetric prescribed mean curvature problems, Two sequences of solutions for indefinite superlinear-sublinear elliptic equations with nonlinear boundary conditions, Unnamed Item, Signed and sign-changing solutions of bi-nonlocal fourth order elliptic problem, The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent, Low and high energy solutions of oscillatory non-autonomous Schrödinger equations with magnetic field, Infinitely many solutions for Kirchhoff-type variable-order fractional Laplacian problems involving variable exponents, Positive solutions for asymptotically linear Schrödinger-Kirchhoff-type equations, Nodal solution for Kirchhoff-type problems with concave-convex nonlinearities, Entire bounded solutions for a class of quasilinear elliptic equations, Existence and multiplicity results for singular quasilinear elliptic equation on unbounded domain, Multiple solutions for asymptotically linear elliptic systems, On finding sign-changing solutions, Periodic solutions of an infinite dimensional Hamiltonian system, Critical point theory on partially ordered Hilbert spaces, Infinitely many homoclinic orbits for a class of second-order damped differential equations, Multiplicity of high energy solutions for superlinear Kirchhoff equations, On a class of Hamiltonian strongly degenerate elliptic systems with concave and convex nonlinearities, Multiplicity of weak solutions to non-local elliptic equations involving the fractional p(x)-Laplacian, Unnamed Item, Multiple solutions for a class of fractional Schrödinger-Poisson system, Multiple solutions for a generalised Schrödinger problem with ``concave-convex nonlinearities, Supercritical problems with concave and convex nonlinearities in ℝN, Multiplicity result for asymptotically linear noncooperative elliptic systems, Infinitely many solutions for a resonant sublinear Schrödinger equation, Infinitely many solutions of $p$-sublinear $p$-Laplacian equations, Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent, On differential systems with strongly indefinite variational structure, Infinitely many solutions for a fractional Kirchhoff type problem via fountain theorem, On the multiplicity of the solutions of the equation $-\Delta u=\lambda \cdot f(u)$, Infinitely many periodic solutions for a class of second-order Hamiltonian systems, Remarks on infinitely many solutions for a class of Schrödinger equations with sign-changing potential, Multiple positive solutions for a Kirchhoff type problem with a critical nonlinearity, Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. I: Algorithms and convergence, Ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth, Existence and multiplicity of solutions for $p(x)$-Laplacian equations in $\mathbb R^N$, High energy solutions for the superlinear Schrödinger-Maxwell equations, On a fourth-order quasilinear elliptic equation of concave-convex type, Multiplicity of solutions of weighted $(p,q)$-Laplacian with small source, Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition, Schrödinger-Poisson systems with radial potentials and discontinuous quasilinear nonlinearity, Generalized Fountain theorem for locally Lipschitz functionals and application, Existence and multiplicity of solutions to concave-convex-type double-phase problems with variable exponent, Radially symmetric solutions for quasilinear elliptic equations involving nonhomogeneous operators in an Orlicz-Sobolev space setting, Estimates for extremal values for a critical fractional equation with concave-convex nonlinearities, On variational and topological methods in nonlinear difference equations, Multiple positive solutions for a class of nonlinear elliptic equations, Sign changing solutions of $p$-fractional equations with concave-convex nonlinearities, Infinitely many solutions of superlinear elliptic equation, On a Neumann problem with critical exponents and Hardy potentials, On Clark's theorem and its applications to partially sublinear problems, A variational principle for problems with a hint of convexity, Positive solutions of nonlinear elliptic equations involving supercritical Sobolev exponents without Ambrosetti and Rabinowitz condition, Critical point theory on convex subsets with applications in differential equations and analysis, Existence and multiplicity results for quasilinear elliptic exterior problems with nonlinear boundary conditions, Symmetric mountain pass lemma and sublinear elliptic equations, Multiple positive solutions for singular elliptic problems involving concave-convex nonlinearities and sign-changing potential, Multiplicity results for variable-order nonlinear fractional magnetic Schrödinger equation with variable growth, Infinitely many homoclinic solutions for second-order Hamiltonian systems with odd nonlinearities, Infinitely many radial solutions to a boundary value problem in a ball, Combined effects in quasilinear elliptic problems with lack of compactness, Infinitely many solutions for a class of quasilinear equation with a combination of convex and concave terms, On the existence of small energy solutions for a sublinear Neumann problem, Combined effects for magnetic Laplace equations with lack of compactness, Multiplicity of solutions for a nonlinear boundary value problem in the upper half-space, Infinitely many homoclinic solutions for a class of second-order Hamiltonian systems, Multiple positive solutions for a critical quasilinear elliptic system with concave-convex nonlinearities, Combined effects in nonlinear problems arising in the study of anisotropic continuous media, Multiple solutions to elliptic equations on $\mathbb{R}^N$ with combined nonlinearities, A note on the positive energy solutions for elliptic equations involving critical Sobolev exponents, The critical Neumann problem for semilinear elliptic equations with concave perturbations, On semilinear biharmonic equations with concave-convex nonlinearities involving weight functions, The effects of concave and convex nonlinearities in some noncooperative elliptic systems, The existence of infinitely many solutions for the nonlinear Schrödinger-Maxwell equations, Existence and multiplicity of solutions for a class of quasilinear elliptic equations: an Orlicz-Sobolev space setting, Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space, Many solutions for elliptic equations with critical exponents, Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave-convex nonlinearity, Existence of a ground state solution for a class of singular elliptic problem in $\mathbb{R}^{N}$, Compact embedding results of Sobolev spaces and existence of positive solutions to quasilinear equations, Anisotropic problems with unbalanced growth, Multiplicity results for elliptic problems with super-critical concave and convex nonlinearties, Robin problems with indefinite linear part and competition phenomena, Multiplicity of solutions for a $p$-Kirchhoff equation, Non-existence and existence of entire solutions for a quasi-linear problem with singular and super-linear terms, Elliptic equations with indefinite concave nonlinearities near the origin, Multiplicity result for a critical elliptic system with concave-convex nonlinearities, Eigenvalue problem with nonstandard growth conditions and involving concave and convex nonlinearities, Existence of infinitely many large solutions for the nonlinear Schrödinger-Maxwell equations, Generalized Fountain Theorem and applications to strongly indefinite semilinear problems, Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case, Periodic solutions of a Dirac equation with concave and convex nonlinearities, On nonlocal existence results for elliptic equations with convex-concave nonlinearities, Infinitely many solutions of Dirac equations with concave and convex nonlinearities, Asymptotically linear Dirac-harmonic maps into flat tori, Multiple solutions for a class of biharmonic equations with a nonlinearity concave at the origin, Some further results on a semilinear equation with concave-convex nonlinearity, Negative energy solutions for a new fractional $p(x)$-Kirchhoff problem without the (AR) condition, Infinitely many solutions for fractional $p$-Kirchhoff equations, On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents, Homoclinic solutions for second order Hamiltonian systems near the origin, On the existence of a continuous branch of nodal solutions of elliptic equations with convex-concave nonlinearities, Infinitely many solutions for elliptic systems with critical exponents, Infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry, On the multiple existence of superquadratic Dirac-harmonic maps into flat tori, A variational approach for the Neumann problem in some FLRW spacetimes, Multiple positive solutions for quasilinear problems with indefinite sublinear nonlinearity, Existence and multiplicity of nontrivial solutions for a semilinear biharmonic equation with weight functions, Weak solutions for a $p$-Laplacian antiperiodic boundary value problem with impulsive effects, Multiple positive solutions for singular elliptic equations with concave-convex nonlinearities and sign-changing weights, Homoclinic solutions for a class of second order Hamiltonian systems with locally defined potentials, The existence of ground state solution to elliptic equation with exponential growth on complete noncompact Riemannian manifold, On multiple solutions of concave and convex nonlinearities in elliptic equation on $\mathbb R^N$, Entire solutions for a quasilinear problem in the presence of sublinear and super-linear terms, On multiple solutions of quasilinear equations involving the critical Sobolev exponent, Periodic solutions of a wave equation with concave and convex nonlinearities, Multiple solutions to $p$-Laplacian problems with concave nonlinearities, A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems, Two sequences of solutions for the semilinear elliptic equations with logarithmic nonlinearities, Multiple solutions for elliptic equations with exponential nonlinearity term combined with convection term in dimension two, On multiple solutions of a singular quasilinear equation on unbounded domain., Nonexistence and existence of nontrivial solutions for Klein-Gordon-Maxwell systems with competing nonlinearities, Laplace's equation with concave and convex boundary nonlinearities on an exterior region, Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation, Existence of solutions to fractional elliptic equation with the Hardy potential and concave-convex nonlinearities, Positive solutions of elliptic and parabolic equations with convex-concave nonlinearities, Existence of infinitely many solutions for sublinear elliptic problems., Modified Trif's functional equations in Banach modules over a $C$-algebra and approximate algebra homomorphisms., An elliptic equation with concave and convex nonlinearities.

Cites Work