Critical points for a class of non-differentiable functions and applications
type: Item
instance of: scholarly article
title: Critical points for a class of non-differentiable functions and applications
zbMATH Open document ID: 1080.49006
author: P. Candito
author: Salvatore A. Marano
author: Dumitru Motreanu
published in: Discrete and Continuous Dynamical Systems
publication date: 2005-06-21T00:00:00Z
review text: Let \(X\) be an infinite dimensional Banach space. This paper is devoted to the study of critical points for functionals of the form \(f=\varphi +\alpha\), where \(\varphi :X\rightarrow \mathbb R\) is locally Lipschitz continuous and \(\alpha :X\rightarrow \mathbb R\cup\{+\infty\}\) is convex, proper and lower semicontinuous. Under some natural assumptions, the main abstract result of the paper establishes the existence of a critical point of \(f\). The corresponding theorem extends a previous result obtained in [\textit{S. Adly, G. Buttazzo} and \textit{M. Théra}, ``Critical points for nonsmooth energy functions and applications'', Nonlinear Anal., Theory Methods Appl. 32, No. 6, 711--718 (1998; Zbl 0940.49019)]. This result is then applied for solving a hemivariational inequality involving a subcritical nonlinearity. The proofs employ refined arguments related to the critical point theory in the sense of Clarke and Chang. The reviewer remarks that the techniques developed in this paper can be extended for solving other classes of nonlinear inequality problems.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 2177519
zbMATH Keywords: hemivariational inequality
zbMATH Keywords: critical point
zbMATH Keywords: locally Lipschitz functional
zbMATH Keywords: existence result
MaRDI profile type: Publication
full work available at URL: dcds.2005.13.175
OpenAlex ID: W2014805109
DOI: 10.3934/DCDS.2005.13.175
description: scientific article; zbMATH DE number 2177519