WELL-POSEDNESS OF A MIXED HEMIVARIATIONAL-VARIATIONAL PROBLEM

We consider a mixed hemivariational-variational problem, i.e., a system which gathers a hemivariational inequality with a constrained variational inequality. We list the assumptions on the data and prove the existence of a unique solution to the problem. Subsequently, we prove the continuous dependence of the solution with respect to the data. Then, we deduce a criterion of convergence to the solution of the mixed hemivariational-variational inequality, i.e., we formulate necessary and sufficient conditions which guarantee the convergence of a sequence to the unique solution of the system. The proof of our results is based on the particular structure of the problem which allows us to employ a fixed point argument. Finally, we provide two examples which illustrate our abstract results.