Variational and Generalized Variational Inequalities with Discontinuous Mappings

In this paper, we derive several existence results for the variational and the generalized variational inequality problems where the mappings under consideration need not have any continuity properties. Uniqueness of the solution of the generalized variational inequality problem is also investigated. As a by-product, we obtain several existence and uniqueness results for the generalized complementarity problem. Applications to minimization problems with generalized convex functions are considered.