International Journal of Nonlinear Analysis and Applications

Existence and controllability for non-instantaneous impulsive stochastic integro-differential equations with noncompact semigroups

Document Type : Research Paper

Authors

1 Laboratory of Mathematics, Modeling and Applications (LaMMA), University of Adrar, ,Algeria

2 Laboratory of Mathematics, Modeling and Applications (LaMMA), University of Adrar, Algeria

3 Laboratory of Mathematics. University of Sidi-Bel-Abbes, Algeria

Abstract

This paper deals with the existence and exact controllability of a class of non-instantaneous impulsive stochastic integro-differential equations with nonlocal conditions in a Hilbert space under the assumption that the semigroup generated by the linear part is noncompact.  A set of sufficient conditions are generated using the stochastic analysis technique,   Kuratowskii's measure of non-compactness, a resolvent operator and a generalized Darbo's fixed point theorem to obtain existence and controllability results of mild solutions for the considered system. Examples are also given to illustrate the effectiveness of controllability results obtained.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 7
July 2023
Pages 1-19
  • Receive Date: 22 November 2022
  • Revise Date: 29 March 2023
  • Accept Date: 29 May 2023