A new critical point theorem for locally Lipschitz functionals with applications to differential equations

DOI10.1016/j.na.2005.12.006zbMath1387.35161OpenAlexW2054171396MaRDI QIDQ858638

Xian Wu

Publication date: 11 January 2007

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.2005.12.006

zbMATH Keywords

critical pointlocally Lipschitz functiongeneralized gradientP.S. condition

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear boundary value problems for ordinary differential equations (34B15) General topics in linear spectral theory for PDEs (35P05) Set-valued operators (47H04) Degenerate elliptic equations (35J70) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Existence and multiplicity of solutions to discrete inclusions with thep(k)-Laplacian problem ⋮ Multiple critical points of saddle geometry functionals ⋮ Multiplicity of solutions to discrete inclusions with the \(p(k)\)-Laplace Kirchhoff type equations ⋮ Existence and multiplicity results for some elliptic systems with discontinuous nonlinearities ⋮ Multiplicity of nontrivial solutions for boundary value problem for impulsive fractional differential inclusions via nonsmooth critical point theory ⋮ Existence and multiplicity of solutions for nonlocal systems involving fractional Laplacian with non-differentiable terms ⋮ A new existence theorem on three critical points for locally Lipschitz functional and an application ⋮ On a class of damped vibration problems with obstacles ⋮ Positive solutions and multiple solutions at non-resonance, resonance and near resonance for hemivariational inequalities with 𝑝-Laplacian ⋮ A Brezis-Nirenberg splitting approach for nonlocal fractional equations

Cites Work

• Unnamed Item
• Unnamed Item
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Remarks on finding critical points
• Analytic methods for approximate solution of elliptic free boundary problems
• A New Approach to Lagrange Multipliers
• The obstacle problem and partial differential equations with discontinuous nonlinearities
• On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems

This page was built for publication: A new critical point theorem for locally Lipschitz functionals with applications to differential equations