Well-posedness of second order differential mixed inverse Quasi-variational inequalities

Abstract

In this paper, we focus on the strong well-posedness and well-posedness in the generalized sense for a kind of second order differential mixed inverse quasi-variational inequalities (DMIQVIs) in Hilbert spaces. Using the approximating solution sequence, we characterize the sufficient and necessary conditions related to the metric characterizations and the strong well-posedness of DMIQVIs under suitable conditions. With respect to the well-posedness in the generalized sense for DMIQVIs, we provide the equivalent conditions by means of the Hausdorff metric and measure of noncom-pactness.