Existence and controllability for some random integrodifferential equations with state-dependent delay

Abstract

In this work, we study the existence, uniqueness of mild solutions and controllabilty outcomes for random integrodifferential equations with state-depend delay. We assume that the nonlinear term is of Carath ́eodory type and satisfies some weakly compactness conditions, we establish results on the existence and uniqueness of mild solutions. Ours analysis uses stochastic analysis theory, Darbo’s fixed point Theorem, M ̈onch’s fixed point Theorem, a random fixed point with stochastic domain and Grimmer’s resolvent operator Theory. At the end, the obtained results are illustrated by an example.