On the Index of Solvability for Variational Inequalities in Banach Spaces

Abstract

We define the index of solvability, a topological characteristic, whose difference from zero provides the existence of a solution for variational inequalities of Stampacchia’s type with S+-type and pseudo-monotone multimaps on reflexive separable Banach spaces. Some applications to a minimization problem and to a problem of economical dynamics are presented.