Electron. J. Diff. Eqns., Vol. 2004(2004), No. 57, pp. 1-17.

Existence and comparison results for quasilinear evolution hemivariational inequalities

Siegfried Carl, Vy K. Le, & Dumitru Motreanu

We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness and extremality results for the hemivariational inequalities under considerations.

Submitted November 17, 2003. Published April 13, 2004.
Math Subject Classifications: 35A15, 35K85, 49J40.
Key Words: Evolution hemivariational inequality, quasilinear, subsolution, supersolution, extremal solution, existence, comparison, compactness.

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Siegfried Carl
Fachbereich Mathematik und Informatik, Institut fur Analysis
Martin-Luther - Universitat Halle-Wittenberg
06099 Halle, Germany
email: carl@mathematik.uni-halle.de   Tel: +49 345 5524639 Fax: +49 345 5527003

Vy K. Le
Department of Mathematics and Statistics
University of Missouri - Rolla, Rolla, MO 65401, USA
email: vy@umr.edu

Dumitru Motreanu
Departement de Mathematiques, Universite de Perpignan
52 Avenue Paul Alduy, 66860 Perpignan, France
email: motreanu@univ-perp.fr

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