ON THE EXISTENCE OF SOLUTIONS OF VARIATIONAL INEQUALITIES IN NONREFLEXIVE BANACH SPACES

We are concerned in this article with an existence theorem for variational inequalities in nonreflexive Banach spaces with a general coercivity condition. The variational inequalities contain multivalued generalized pseudomonotone mappings and convex functionals, the nonreflexive Banach spaces form a complementary system, and the coercivity condition involves both the mapping and the functional. As an application, we study second-order elliptic variational inequalities with multivalued lower-order terms in general Orlicz-Sobolev spaces.