Existence and comparison principles for general quasilinear variational–hemivariational inequalities

Abstract

We consider quasilinear elliptic variational–hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. 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.