Journal of Inequalities and Applications
Volume 2005 (2005), Issue 2, Pages 89-105

Existence and infinitely many solutions for an abstract class of hemivariational inequalities

Csaba Varga

Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 Mihail Kogǎlniceanu Street, Cluj-Napoca 400084 , Romania

Received 1 June 2003; Revised 4 January 2005

Copyright © 2005 Csaba Varga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract class contains some special cases studied by many authors. We remark that, differently from the classical literature, in the proofs we use the Cerami compactness condition and the principle of symmetric criticality for locally Lipschitz functions.