The (S)+ condition on generalized variational inequalities

In this paper, we derive some existence results for generalized variational inequalities associated with mappings satisfying the (S)+ condition. The relation between the (S)+ and (S)+1 conditions is discussed. As an application, we also consider multivalued complementarity problems associated with mappings satisfying the (S)+ condition, and prove a theorem to characterize the solvability of such problems in terms of exceptional families of elements.