Existence of solutions for implicit obstacle problems involving nonhomogeneous partial differential operators and multivalued terms

Abstract

In this article, we study an implicit obstacle problem with a nonlinear nonhomogeneous partial differential operator and a multivalued operator which is described by a generalized gradient. Under quite general assumptions on the data, and employing Kluge's fixed point principle for multivalued operators, Minty technique and a surjectivity theorem, we prove that the set of weak solutions to the problem is nonempty, bounded and weakly closed.