Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 79532, 13 pages

Existence results for nonlocal and nonsmooth hemivariational inequalities

S. Carl1 and S. Heikkilä2

1Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität Halle-Wittenberg, Halle 06099, Germany
2Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Finland

Received 4 May 2005; Accepted 10 May 2005

Copyright © 2006 S. Carl and S. Heikkilä. 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.


We consider an elliptic hemivariational inequality with nonlocal nonlinearities. Assuming only certain growth conditions on the data, we are able to prove existence results for the problem under consideration. In particular, no continuity assumptions are imposed on the nonlocal term. The proofs rely on a combined use of recent results due to the authors on hemivariational inequalities and operator equations in partially ordered sets.