Stability analysis of partial differential variational inequalities in Banach spaces

In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques

A class of generalized evolutionary problems driven by variational inequalities and fractional operators

This paper is devoted to a generalized evolution system called fractional partial differential variational inequality which consists of a mixed quasi-variational inequality combined with a fractional partial differential equation in a Banach space. Invoking the pseudomonotonicity of multivalued operators and a generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, first, we prove that the solution set of the mixed quasi-variational inequality involved in system is nonempty, closed and convex. Next, the measurability and upper semicontinuity for the mixed quasi-variational inequality with respect to the time variable and state variable are established. Finally, the existence of mild solutions for the system is delivered. The approach is based on the theory of operator semigroups, the Bohnenblust-Karlin fixed point principle for multivalued mappings, and theory of fractional operators