A multiplicity result for hemivariational inequalities
type: Item
instance of: scholarly article
title: A multiplicity result for hemivariational inequalities
zbMATH Open document ID: 1116.49009
author: Francesca Faraci
author: Antonio Iannizzotto
author: Csaba Varga
author: Hannelore Lisei
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-10T00:00:00Z
review text: Let \(\Omega\) be an unbounded domain in \(R^{N},X\) be a Banach space (compactly embedded in some space \(L^{r}(\Omega),A\) the duality mapping on \(X\) induced by the weight function \(t\rightarrow t^{p-1}(1<p<N),F:\mathbb{R}\rightarrow \mathbb{R}\) a locally Lipschitz function with generalized derivative \(F^{0}:\) \[ F^{0}(x;y)=\lim_{z\rightarrow x}\sup_{\tau\rightarrow 0+}\frac{F(z+\tau y)-F(z)}{\tau}, \] \(b:\Omega \rightarrow \mathbb{R}\) a non-negative function. In this work it is proved the existence such \(u_0\in X\) and \(\lambda>0\) that the hemivariational inequality \[ <A(u-u_0)>+\lambda \int_{\Omega}b(x)F^{0}(u(x;-v(x)))dx\geq 0,\forall v\in X \] admits at least three solutions in \(X\). As applications of the general result in Sobolev spaces some variational inequalities are considered.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 5141611
zbMATH Keywords: hemivariational inequalities
zbMATH Keywords: locally Lipschitz functions
reviewed by: T. Tadumadze
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.07.081
OpenAlex ID: W1993406619
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DOI: 10.1016/J.JMAA.2006.07.081
description: scientific article; zbMATH DE number 5141611