VARIATIONAL INEQUALITIES FOR PERTURBATIONS OF MAXIMAL MONOTONE OPERATORS IN REFLEXIVE BANACH SPACES

Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X*, and let K be a nonempty, closed and convex subset of X with 0 in its interior. Let T be maximal monotone and S a possibly unbounded pseudomonotone, or finitely continuous generalized pseudomonotone, or regular generalized pseudomonotone operator with domain K. Let phi be a proper, convex and lower semicontinuous function. New results are given concerning the solvability of perturbed variational inequalities involving the operator T + S and the function phi. The associated range results for nonlinear operators are also given, as well as extensions and/or improvements of known results of Kenmochi, Le, Browder, Browder and Hess, De Figueiredo, Zhou, and others.