Journal of Inequalities and Applications
Volume 2005 (2005), Issue 1, Pages 33-40

Existence and comparison results for variational-hemivariational inequalities

S. Carl

Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität Halle-Wittenberg, Halle 06099, Germany

Received 18 June 2004

Copyright © 2005 S. Carl. 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 a prototype of quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities. Furthermore, we give an example to illustrate the abstract theory developed in this paper.