Existence and localization results for \(p(x)\)-Laplacian via topological methods

DOI10.1155/2010/120646zbMath1198.35109OpenAlexW2154418746WikidataQ59253715 ScholiaQ59253715MaRDI QIDQ1958012

Rabil Ayazoglu (Mashiyev), Bilal Cekic

Publication date: 28 September 2010

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/224857

zbMATH Keywords

Dirichlet problemweak solution\(p(x)\)-Laplacian

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Degenerate elliptic equations (35J70) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

Related Items (17)

Existence and multiplicity of the solutions of the p (x )-Kirchhoff type equation via genus theory ⋮ Operator equations and duality mappings in Sobolev spaces with variable exponents ⋮ Positive solutions for the \(p(x)-\)Laplacian : application of the Nehari method ⋮ Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations ⋮ Small perturbations of critical nonlocal equations with variable exponents ⋮ A critical \(p(x)\)-Laplacian Steklov type problem with weights ⋮ Solutions of nonlocal \((p_1(x),p_2(x))\)-Laplacian equations ⋮ The fibering map approach to a nonlocal problem involving \(p(x)\)-Laplacian ⋮ Sign changing solutions of the \(p(x)\)-Laplacian equation ⋮ Existence results for a class of nonlocal problems involving \(p(x)\)-Laplacian ⋮ The multiplicity of nontrivial solutions for a new \(p(x)\)-Kirchhoff-type elliptic problem ⋮ On a class of \(p(x)\)-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions ⋮ On a Robin type problem involving \(p(x)\)-Laplacian operator ⋮ Robin problems involving the \(p(x)\)-Laplacian ⋮ On a class of critical p(x)-Laplacian type problems with Steklov boundary conditions ⋮ Regularity results for nonlinear parabolic problems in variable exponent Sobolev space with degenerate coercivity ⋮ Positive periodic solutions of nonlinear differential equations system with nonstandard growth

Cites Work

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• A fixed point method for the \(p(\cdot\))-Laplacian
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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