A Variational Principle for Equations and Inequalities with Maximal Monotone Operators

Abstract

Let be given a variational inequality with a monotone operator. We describe the set of solutions by a modified variational principle. This still remains valid if the operator is not a subdifferential of a convex function. It allows a physical interpretation and shows in which sense the monotonicity of the operator leads to "globally stable" solutions of the variational in equality.