Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem

DOI10.1016/j.na.2009.08.029zbMath1184.35316OpenAlexW1991837007MaRDI QIDQ2653970

Guowei Dai

Publication date: 15 January 2010

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.2009.08.029

zbMATH Keywords

nonsmooth analysisFountain theoremdifferential inclusion problemdual Fountain theorem

Mathematics Subject Classification ID

PDEs with multivalued right-hand sides (35R70) Nonlinear elliptic equations (35J60) Existence of solutions for minimax problems (49J35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Weak solutions to PDEs (35D30) Optimality conditions for minimax problems (49K35) Variational methods for second-order elliptic equations (35J20)

Related Items (16)

Solutions for a degenerate \(p(x)\)-Laplacian equation with a nonsmooth potential ⋮ Generalized Fountain theorem for locally Lipschitz functionals and application ⋮ Strauss' and Lions' type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem ⋮ Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods ⋮ Existence of solutions for a differential inclusion problem with singular coefficients involving the \(p(x)\)-Laplacian ⋮ Infinitely many periodic solutions for some second-order differential systems with \(p(t)\)-Laplacian ⋮ Existence and multiplicity results for a class of fractional differential inclusions with boundary conditions ⋮ Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials ⋮ Existence and multiplicity results for anisotropic double-phase differential inclusion with unbalanced growth and lack of compactness ⋮ Existence and multiplicity of solutions for a quasilinear nonlocal problem ⋮ Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions ⋮ Unnamed Item ⋮ Existence and multiplicity of solutions for a quasilinear elliptic inclusion with a nonsmooth potential ⋮ On existence and multiplicity of solutions for Kirchhoff-type equations with a nonsmooth potential ⋮ Infinitely many solutions for a non-homogeneous differential inclusion with lack of compactness ⋮ Homoclinic solutions for a differential inclusion system involving the \(p(t)\)-Laplacian

Cites Work

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• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Nonsmooth critical point theory and nonlinear elliptic equations at resonance
• On a three critical points theorem
• Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the \(p\)-Laplacian
• Minimax theorems
• A general variational principle and some of its applications
• Infinitely many solutions for a differential inclusion problem in \(\mathbb R^N\)
• Infinitely many solutions of a symmetric Dirichlet problem
• On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems

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