On the existence of positive solutions for hemivariational inequalities driven by the \(p\)-Laplacian

DOI10.1007/s10898-003-5444-3zbMath1330.35180OpenAlexW2037291150WikidataQ112251848 ScholiaQ112251848MaRDI QIDQ555997

Leszek Gasiński, Nikolaos S. Papageorgiou, Michael E. Filippakis

Publication date: 13 June 2005

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-003-5444-3

zbMATH Keywords

hemivariational inequalitypositive solutionnonsmooth critical point theory\(p\)-LaplacianClarke subdifferentialnonsmooth Cerami conditionnonsmooth Mountain Pass Theoremprincipal eigenvalue and eigenfunction

Mathematics Subject Classification ID

Variational inequalities (49J40) PDEs with multivalued right-hand sides (35R70) Nonlinear boundary value problems for linear elliptic equations (35J65) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)

Related Items (11)

Existence and concentration of positive solutions for a class of discontinuous quasilinear Schrödinger problems in \(\mathbb{R}^N \) ⋮ Solutions for a degenerate \(p(x)\)-Laplacian equation with a nonsmooth potential ⋮ Existence and convergence results for an elastic frictional contact problem with nonmonotone subdifferential boundary conditions ⋮ A pair of positive solutions for \((p, q)\)-equations with combined nonlinearities ⋮ A pair of positive solutions for the Dirichlet \(p(z)\)-Laplacian with concave and convex nonlinearities ⋮ Multiple solutions for inequality Dirichlet problems by the \(p(x)\)-Laplacian ⋮ Periodic solutions for a differential inclusion problem involving the \(p(t)\)-Laplacian ⋮ Unnamed Item ⋮ Existence and multiplicity of solutions for \(p(x)\)-Laplacian equation with nonsmooth potential ⋮ Sensitivity analysis of optimal control problems driven by dynamic history-dependent variational-hemivariational inequalities ⋮ Multiplicity of solutions for a class of \((p_1,p_2,\ldots,p_n)\)-Laplacian elliptic systems with a nonsmooth potential

Cites Work

• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Mountain pass theorems for non-differentiable functions and applications
• Double eigenvalue problems for hemivariational inequalities
• Superlinear elliptic boundary value problems
• Dual variational methods in critical point theory and applications
• A strong maximum principle for some quasilinear elliptic equations
• Linear and quasilinear elliptic equations
• An existence theorem for nonlinear hemivariational inequalities at resonance
• Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance
• On the Existence of Positive Solutions for a Class of Semilinear Elliptic Boundary Value Problems
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Optimization and nonsmooth analysis
• Boundary regularity for solutions of degenerate elliptic equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• On a class of superlinear elliptic problems
• Eigenvalue problems for variational-hemivariational inequalities at resonance
• Variational elliptic problems which are nonquadratic at infinity
• Existence of asymptotically linear Dirichlet problem
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