Well-posedness of a class of generalized mixed hemivariational-variational inequalities

Abstract The purpose of this paper is to investigate a class of generalized mixed hemivariational–variational inequalities of elliptic type in a Banach space. A well-posedness result for the inequality is obtained, including existence, uniqueness, and stability of solution. The approach is based on a set-valued fixed point theorem combined with the theory of nonsmooth analysis. An elastic contact problem with the constitutive law involving a convex subdifferential inclusion is considered as an illustrative application, in which the contact boundary conditions are described by a unilateral frictionless contact condition, and a bilateral multivalued frictional contact law.