Existence and multiplicity of solutions for a general \(p(x)\)-Laplacian Neumann problem

DOI10.1016/j.na.2008.07.027zbMath1170.34311OpenAlexW1967896620MaRDI QIDQ1012086

Xiayang Shi, Xuanhao Ding

Publication date: 14 April 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.07.027

zbMATH Keywords

\(p(x)\)-Laplacian

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15)

Related Items (16)

Three solutions for a nonlinear Neumann boundary value problem ⋮ Existence of solutions for a Robin problem involving the \(p(x)\)-Laplace operator ⋮ Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem ⋮ Existence results for a Neumann problem involving the \(p(x)\)-Laplacian with discontinuous nonlinearities ⋮ Existence and multiplicity of solutions for anisotropic elliptic equation ⋮ Unnamed Item ⋮ Three solutions to a Steklov problem involving the weighted \(p(\cdot)\)-Laplacian ⋮ A note on the Neumann problem ⋮ Unnamed Item ⋮ Multiplicity results of \(p(x)\)-Laplacian systems with Neumann conditions ⋮ Multiple solutions for elliptic \((p(x), q(x))\)-Kirchhoff-type potential systems in unbounded domains ⋮ Multiple solutions for a class of Neumann doubly eigenvalue boundary value systems involving the \((p_1(x),\dots,p_n(x))\)-Laplacian ⋮ Unnamed Item ⋮ Existence of three solutions for a Neumann problem involving thep(x)-Laplace operator ⋮ Robin problems involving the \(p(x)\)-Laplacian ⋮ Unnamed Item

Cites Work

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• Orlicz spaces and modular spaces
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• On a three critical points theorem
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• A general variational principle and some of its applications
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• OnL^p(x)norms
• Sobolev embeddings with variable exponent
• On a class of nonlinear variational–hemivariational inequalities
• 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
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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