Critical point theory for nonsmooth functionals

DOI10.1016/j.na.2006.04.003zbMath1117.58008OpenAlexW2042237041MaRDI QIDQ876949

Yuxia Guo, Jia Quan Liu

Publication date: 19 April 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.2006.04.003

zbMATH Keywords

quasilinear equationsaddle point theoremdeformation lemma

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (15)

Quasilinear Schrödinger equations involving singular potentials ⋮ A nonsmooth theory for a logarithmic elliptic equation with singular nonlinearity ⋮ Existence and multiplicity results for a class of fractional differential inclusions with boundary conditions ⋮ On Clark's theorem and its applications to partially sublinear problems ⋮ Periodic solutions of second-order differential inclusions systems with \(p(t)\)-Laplacian ⋮ Parameter-dependent multiplicity results of sign-changing solutions for quasilinear elliptic equations ⋮ Multibump solutions for quasilinear elliptic equations ⋮ A Variant of Clark's Theorem and Its Applications for Nonsmooth Functionals without the Palais--Smale Condition ⋮ Existence and subharmonicity of solutions for nonlinear non-smooth periodic systems with a \(p\)-Laplacian ⋮ Solutions for singular \(p\)-Laplacian equation in \(R^{n}\) ⋮ A variant of Clark's theorem and its applications for nonsmooth functionals without the global symmetric condition ⋮ Multiple solutions of a parameter-dependent quasilinear elliptic equation ⋮ Multibump solutions for quasilinear elliptic equations with critical growth ⋮ Existence results for a singular quasilinear elliptic equation ⋮ Low perturbations and combined effects of critical and singular nonlinearities in Kirchhoff problems

Cites Work

• Quasilinear elliptic eigenvalue problems
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• A critical point theory for nonsmooth functionals
• Infinite dimensional Morse theory and multiple solution problems
• A generalized saddle point theorem
• Mountain pass theorems and global homeomorphism theorems
• Morse theory for continuous functionals
• Metric critical point theory. I: Morse regularity and homotopic stability of a minimum
• Dual variational methods in critical point theory and applications
• Critical point theory for nondifferentiable functionals and applications
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