Existence of Solutions for Non-Autonomous Second-Order Stochastic Inclusions with Clarke's Subdifferential and non Instantaneous Impulses

Abstract

This manuscript explores a new class of non-autonomous second-order stochastic inclusions of Clarke's subdifferential form with non-instantaneous impulses (NIIs), unbounded delay and the Rosenblatt process in Hilbert spaces. The existence of a solution is deduced by employing a fixed point strategy for a set-valued map together with the evolution operator and stochastic analysis approach. An example is analyzed for theoretical developments.