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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Vy K. Le
Department of Mathematics and Statistics
University of Missouri - Rolla, Rolla, MO 65401, USA
Departement de Mathematiques, Universite de Perpignan
52 Avenue Paul Alduy, 66860 Perpignan, France