International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 401-417
doi:10.1155/IJMMS.2005.401
Existence, comparison, and compactness results for quasilinear variational-hemivariational inequalities
S. Carl1
, Vy K. Le2
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
Abstract
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.