A class of differential inverse quasi-variational inequalities in finite dimensional spaces

In this paper, we introduce and study a class of differential inverse quasi-variational inequalities in finite dimensional Euclidean spaces, which are closely related to the differential variational inequalities. By using two important theorems on differential inclusions, we first prove some existence theorems for Caratheodory weak solutions of the differential inverse quasivariational inequality considered. Then, with the Euler computation method, we construct an Euler time-dependent scheme for solving the differential inverse quasi-variational inequality and prove a convergence result on the Euler time-dependent scheme constructed.