Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces

Abstract

We consider the existence of solutions of variational inequality form. Find u∈D(J):〈A(u),v-u〉+〈F(u),v-u〉+J(v)-J(u)≥0, ∀v∈W1LM(Ω), whose principal part is having a growth not necessarily of polynomial type, where A is a second-order elliptic operator of Leray-Lions type, F is a multivalued lower order term, and J is a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces.