Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem

DOI10.1016/j.ajmsc.2012.09.006zbMath1284.35195OpenAlexW2007234808MaRDI QIDQ375177

F. Kissi, Abdelrachid El Amrouss

Publication date: 28 October 2013

Published in: Arab Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: http://www.sciencedirect.com/science/article/pii/S1319516612000345

zbMATH Keywords

Sobolev spaceweak solutionmountain pass theoremmultiple solutionsvariational methodAmbrosetti-Rabinowitz condition\(p(x)\)-Laplace operatorgeneralized Lebesgue-Sobolev spacesnonlinear Dirichlet problems

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Weak solutions to PDEs (35D30) Quasilinear elliptic equations with (p)-Laplacian (35J92) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items (4)

Unnamed Item ⋮ Ground state solutions for a kind of superlinear elliptic equations with variable exponent ⋮ Anisotropic discrete boundary value problems ⋮ Ground state solutions for a class of elliptic Dirichlet problems involving the \(p(x)\)-Laplacian

Cites Work

• Unnamed Item
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• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
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• Multiplicity results for quasi-linear problems
• Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
• Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• OnL^p(x)norms
• Sobolev embeddings with variable exponent
• Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian
• Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator

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