Existence of mild solutions for stochastic integro-differential equations using fixed point approach

Abstract

 This paper investigates a class of nonlinear Itô-type stochastic integro-differential equations in Hilbert spaces incorporating constant delay, neutral terms, impulsive perturbations, and nonlocal initial constraints. By employing the Kuratowski measure of noncompactness together with Sadovskii’s fixed-point theorem, new sufficient criteria are established for the existence and uniqueness of mild solutions within a condensing operator setting. An illustrative example is presented to validate the theoretical findings and demonstrate the practical applicability of the obtained results.