Title: Existence results on impulsive stochastic semilinear differential inclusions

Authors: Mustapha Meghnafi; Mohamed Ali Hammami; Tayeb Blouhi

Addresses: Department of Mathematics and Computer Science, University of Bechar, P.O.Box 417, Bechar, 08000, Algeria ' Department of Mathematics, University of Sfax, Tunisie ' Department of Mathematics, Usto University, Oran 31000, Algeria

Abstract: 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.

Keywords: mild solutions; periodic solutions; impulses; matrix convergent to zero; generalised Banach space; Poisson jumps; fixed point; set-valued analysis; differential inclusions.

DOI: 10.1504/IJDSDE.2021.115179

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.2, pp.131 - 159

Received: 08 Sep 2018
Accepted: 07 May 2019

Published online: 24 May 2021 *

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