International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 401-417

Existence, comparison, and compactness results for quasilinear variational-hemivariational inequalities

S. Carl,1 Vy K. Le,2 and D. Motreanu3

1Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität, Halle-Wittenberg, Halle 06099, Germany
2Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla 65401, MO, USA
3Département de Mathématiques, Université de Perpignan, 52 Avenue Paul Alduy, Perpignan 66860, France

Received 31 May 2004; Revised 9 November 2004

Copyright © 2005 S. Carl et al. 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 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, including existence, comparison, compactness, and extremality results.