Existence and multiplicity of solutions for a class of elliptic equations without Ambrosetti-Rabinowitz type conditions

DOI10.1007/s10884-016-9542-6zbMath1400.35126OpenAlexW2731490907MaRDI QIDQ1663160

E. Juárez Hurtado, Rodrigo Da Silva Rodrigues, Olímpio Hiroshi Miyagaki

Publication date: 21 August 2018

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-016-9542-6

zbMATH Keywords

Sobolev spacesquasilinear equationDirichlet condition\(p(\cdot )\)-Laplace-type operators

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods applied to PDEs (35A15) Quasilinear elliptic equations (35J62) Boundary value problems for higher-order elliptic systems (35J58)

Related Items (18)

Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent ⋮ Existence and multiplicity of solutions for Schrödinger-Kirchhoff type problems involving the fractional \(p(\cdot) \)-Laplacian in \(\mathbb{R}^N\) ⋮ Fractional double phase Robin problem involving variable order-exponents without Ambrosetti-Rabinowitz condition ⋮ Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition ⋮ 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 ⋮ Small perturbations of critical nonlocal equations with variable exponents ⋮ Existence of infinitely many weak solutions to Kirchhoff–Schrödinger–Poisson systems and related models ⋮ Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent ⋮ Weak solvability of nonlinear elliptic equations involving variable exponents ⋮ Fractional weighted \(p\)-Kirchhoff equations with general nonlinearity ⋮ Existence and multiplicity of solutions for (p,q)$$ \left(p,q\right) $$‐Laplacian Kirchhoff‐type fractional differential equations with impulses ⋮ GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION ⋮ A class of elliptic equations involving nonlocal integrodifferential operators with sign-changing weight functions ⋮ Infinitely many solutions for double phase problem with unbounded potential in \(\mathbb{R}^N\) ⋮ Existence and multiplicity of solutions for a class of \((p,q)\)-Laplacian equations in \(\mathbb{R}^N\) with sign-changing potential ⋮ Multiplicity of weak solutions to non-local elliptic equations involving the fractional p(x)-Laplacian ⋮ On a class of \(p(x)\)-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions

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