Existence and Uniqueness of Mild Solutions of Stochastic Partial Integro-Differential Impulsive Equations with Infinite Delay via Resolvent Operator

Abstract

In this paper, we investigate the existence of mild solutions for a class of stochastic functional differential impulsive equations with infinite delay on Hilbert space. The results are obtained by using the Banach fixed point theorem and Krasnoselskii-Schaefer type fixed point theorem combined with theories of resolvent operators. In the end as an application, an example has been presented to illustrate the results obtained.

Existence and controllability results for an impulsive stochastic integro-differential equations with state-dependent delay

“…However, it will not be a semigroup since it does not satisfy the semigroup properties. The existence, uniqueness, stability, controllability, and other quantitative and qualitative aspects of stochastic integrodifferential equations have recently attracted much attention (see [6,[12][13][14]37]). In many cases, deterministic models will fluctuate due to random or seemingly random environmental noise.…”