On the pseudo-monotonicity of generalized gradients of nonconvex functions

Abstract

The paper is devoted to study the class of nonconvex, nondifferentiable functionals on a reflexive Banach space whose generalized Clarke's gradient i s pseudo-monotone i n the sense of Browder-Hess. I n particular, it has been proved that on some restrictions functionals expressed as a pointwise minimum of a finite collection of convex functions belong to this class. Results obtained are used to establish some existence theorems for hemivariational inequalities involving superpotentials under consideration.

Keywords:

• Pseudo-monotonicity
• generalized gradient
• hemivariational inequality

AMS:

• 49A29
• 49A52