Existence results on impulsive stochastic semilinear differential inclusions

In this paper, we present some existence results of mild solutions and study the topological structure of solution sets for the following first-order impulsive stochastic semilinear differential inclusions driven by Poisson jumps with periodic boundary conditions. We consider the cases in which the right hand side can be either convex . The results are obtained by using fixed point theorems for multivalued mappings, more precisely, the technique is based on fixed point theorem a nonlinear alternative of Leray-Schauder's fixed point theorem in generalised metric and Banach spaces.