Convergence Results for Elliptic Variational-Hemivariational Inequalities

We consider an elliptic variational-hemivariational inequality P in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {P-n} of variational-hemivariational inequalities such that, for each n is an element of N, inequality P-n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter epsilon(n). The unique solvability of P and, for each n is an element of N, the solvability of its perturbed version P-n, are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem P and, for each n is an element of N, let u(n) be a solution of Problem P-n. The main result of this paper states the strong convergence of u(n) -> u in X, as n -> infinity. We show that the main result extends a number of results previously obtained in the study of Problem Y. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations.