Levitin–Polyak well-posedness of variational–hemivariational inequalities

Abstract

In this paper we consider the Levitin–Polyak well-posedness of a variational–hemivariational inequality in reflexive Banach spaces. First, we establish the equivalence between the Levitin–Polyak well-posedness of the considered inequality and the existence and uniqueness of its solution. Then, we discuss the relationships among the Levitin–Polyak well-posedness of the variational–hemivariational inequality, its corresponding inclusion problem and a constrained minimization problem. The proof of our results are based on arguments of monotonicity, convexity and the properties of the Clarke generalized gradient. Finally, we provide an application of our results in the study of a frictional contact problem with subdifferential boundary conditions.