On variational and quasi-variational inequalities with multivalued lower order terms and convex functionals.

Abstract: In this paper, we consider the existence and some qualitative properties of solutions of variational inequalities of the form: and of quasi-variational inequalities of the form: where is a second-order elliptic operator of Leray–Lions type, is a multivalued lower order term, and are convex functionals, and also depends on . We concentrate here in noncoercive cases and use sub-supersolution methods to study the existence and enclosure of solutions, and also the existence of extremal solutions between sub and supersolutions. [Copyright &y& Elsevier]