A multiplicity result for \(p(x)\)-Laplacian problem in \(\mathbb R^N\)

DOI10.1016/j.na.2008.03.038zbMath1156.35363OpenAlexW1569483525MaRDI QIDQ1004621

Yongqiang Fu, Xia Zhang

Publication date: 11 March 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.2008.03.038

zbMATH Keywords

critical pointvariable exponent Sobolev space\(p(x)\)-Laplacian problem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60)

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Cites Work

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• Existence of radial solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Existence of solutions for \(p(x)\)-Laplacian problem on an unbounded domain
• On a superlinear elliptic \(p\)-Laplacian equation.
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Minimax theorems
• The quasi-minimizer of integral functionals with \(m(x)\) growth conditions
• Nonhomogeneous boundary value problems in anisotropic Sobolev spaces
• Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
• Nonlinear p-Laplacian Problems on Unbounded Domains
• OnL^p(x)norms
• Existence of multiple non-trivial solutions for nonlinear p-Laplacian problems on ℝ^N
• Sobolev embeddings with variable exponent
• Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)