Multiple solutions for inequality Dirichlet problems by the \(p(x)\)-Laplacian

DOI10.1016/j.nonrwa.2009.11.014zbMath1196.35236OpenAlexW1973235171MaRDI QIDQ984608

Bin Ge, Xiao-Ping Xue

Publication date: 20 July 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.2009.11.014

zbMATH Keywords

integral functionalsDirichlet problem\(p(x)\)-Laplacianvariable exponent Sobolev space

Mathematics Subject Classification ID

PDEs with multivalued right-hand sides (35R70) Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)

Related Items (7)

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 ⋮ On the solvability of variable exponent differential inclusion systems with multivalued convection term ⋮ Multiple solutions for a class of differential inclusion system involving the \((p(x), q(x))\)-Laplacian ⋮ Three solutions for a differential inclusion problem involving thep(x)-Kirchhoff-type ⋮ Existence and nonexistence of solutions for the double phase problem ⋮ Multiple solutions to a class of \(p(x)\)-biharmonic differential inclusion problem with no-flux boundary condition

Cites Work

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• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequali\-ties
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance
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• Two nontrivial critical points for nonsmooth functionals via local linking and applications
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• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Elliptic Partial Differential Equations of Second Order
• A multiplicity theorem for problems with the \(p\)-Laplacian
• Compact imbedding theorems with symmetry of Strauss-Lions type for the space \(W^{1,p(x)}(\Omega)\)
• Regularity results for a class of functionals with non-standard growth
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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