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


Amadou Diop, Mbarack Fall, Mamadou Abdoul Diop, Khalil Ezzinbi




The goal of this study is to investigate the existence and uniqueness of mild solutions, as well as controllability outcomes, for random integrodifferential equations with state-dependent delay. We prove the existence and uniqueness of mild solutions in the case where the nonlinear term is of the Carathéodory type and meets various weakly compactness conditions. Our research is based on Dardo's fixed point theorem, Mönch's fixed point theorem, a random fixed point with a stochastic domain, and Grimmer's resolvent operator theory. Finally, an example is provided to demonstrate the outcomes that were obtained