The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities

Abstract

We generalize the sub-supersolution method known for weak solutions of single and multivalued equations to quasilinear elliptic 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.