Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed variational-hemivariational inequality and give some conditions under which the strongly mixed variational-hemivariational inequality is strongly well-posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational-hemivariational inequality and the well-posedness for the corresponding inclusion problem