Existence and multiplicity of solutions for \(p(x)\)-Laplacian equation with nonsmooth potential

DOI10.1016/j.nonrwa.2008.10.019zbMath1181.35119OpenAlexW2058244643MaRDI QIDQ1049419

Zifei Shen, Chenyin Qian

Publication date: 12 January 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2008.10.019

zbMATH Keywords

nonsmooth critical point theorylocally Lipschitz functional\(p(x)\)-Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Weak solutions to PDEs (35D30) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

Existence of nontrivial solutions for Kirchhoff-type variational inclusion system in \(\mathbb R^N\) ⋮ Solutions for a degenerate \(p(x)\)-Laplacian equation with a nonsmooth potential ⋮ Multiple solutions to a class of inclusion problem with thep(x)-Laplacian ⋮ Infinitely many positive solutions for a differential inclusion problem involving the p(x) -Laplacian ⋮ Extinction behavior of solutions for the \(p\)-Laplacian equations with nonlocal sources ⋮ Multiplicity of solutions on a nonlinear eigenvalue problem for \(p(x)\)-Laplacian-like operators ⋮ On the solvability of variable exponent differential inclusion systems with multivalued convection term ⋮ Existence of at least five solutions for a differential inclusion problem involving the \(p(x)\)-Laplacian ⋮ Multiple solutions for inequality Dirichlet problems by the \(p(x)\)-Laplacian ⋮ Multiple solutions to a class of \(p(x)\)-biharmonic differential inclusion problem with no-flux boundary condition ⋮ EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH ⋮ Infinitely many solutions for a Kirchhoff-type problem with non-standard growth and indefinite weight

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