On solvability of the variational inequality with +-coercive multivalued mappings

Abstract

In this work the theory of variational inequalities with multivalued operators is extended for the wider of multivalued maps from the re°exive Banach space to its dual one. In particular, we relax the restriction on boundness of operators and on same properties of convergence. This operator class contains the bounded pseudomonotone maps, the maximal monotone maps on interior of domain, the s{weakly locally bounded generalized pseudomonotone maps and other.