Well-posedness for a Class of Variational-Hemivariational Inequalities with Perturbations

In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational-hemivariational inequality and give some conditions under which the variational-hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational-hemivariational inequality and the well-posedness of corresponding inclusion problem.