On the well-posedness of differential mixed quasi-variational-inequalities

Abstract

We discuss the well-posedness and the well-posedness in the generalized sense of differential mixed quasi-variational inequalities ((DMQVIs), for short) in Hilbert spaces. This gives us an outlook to the convergence analysis of approximating sequences of solutions for (DMQVIs). Using these concepts we point out the relation between metric characterizations and well-posedness of (DMQVIs). We also prove that the solution set of (DMQVIs) is compact, if problem (DMQVIs) is well-posed in the generalized sense.