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.
"On the existence of solutions of variational inequalities in nonreflexive Banach spaces." Banach J. Math. Anal. 13 (2) 293 - 313, April 2019. https://doi.org/10.1215/17358787-2018-0034