J. Math. Anal. Appl. 330 (2007) 683–698 www.elsevier.com/locate/jmaa A multiplicity result for hemivariational inequalities Francesca Faraci a , Antonio Iannizzotto a , Hannelore Lisei b,∗,1 , Csaba Varga b,2 a Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6, 95125 Catania, Italy b Faculty of Mathematics and Computer Sciences, Babe¸ s-Bolyai University, Str. Kog˘ alniceanu nr. 1, 400084 Cluj-Napoca, Romania Received 26 March 2006 Available online 7 September 2006 Submitted by V. Radulescu Abstract In this paper we extend a multiplicity result of Ricceri to locally Lipschitz functionals and prove the existence of multiple solutions for a class of hemivariational inequalities.  2006 Elsevier Inc. All rights reserved. Keywords: Locally Lipschitz functions; Principle of symmetric criticality; Hemivariational inequalities 1. Introduction The present paper yields some multiplicity results for a class of hemivariational inequalities on unbounded domains. This problem is studied via variational methods: Clarke’s theory of differentiation for locally Lipschitz functionals on Banach spaces is employed, in conjunction with some results in the theory of best approximation in Banach spaces. A link between best approximation and the (classical) critical point theory was established in the recent works of Tsar’kov [19] and Ricceri [18]. In the latter it is proved that, given a continuously Gâteaux differentiable functional J defined over a real Hilbert space X, for each * Corresponding author. E-mail addresses: ffaraci@dmi.unict.it (F. Faraci), iannizzotto@dmi.unict.it (A. Iannizzotto), hanne@math.ubbcluj.ro (H. Lisei), csvarga@cs.ubbcluj.ro (C. Varga). 1 This work was partially supported by MEdC-ANCS, research project CEEX 2983/11.10.2005. 2 This author was partially supported by the Research Center of Sapientia Foundation, Project No. 1239. 0022-247X/$ – see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jmaa.2006.07.081