Square mean asymptotically \(\varkappa\)-periodic solution for stochastic integro-differential equations via the degree of nondensifiability

Abstract

In this paper, we explore square-mean asymptotically \(\varkappa\)-periodic mild solutions from square mean \(\varkappa\)-periodic limit for a stochastic integro-differential equations driven by Brownian motion, utilizing Grimmer’s resolvent and a version of Darbo’s fixed point theorem based on the degree of nondensifiability. Additionally, an example is given to illustrate our results.