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

TL;DR

This paper establishes the existence of solutions for a new class of non-autonomous second-order stochastic inclusions involving Clarke's subdifferential, NIIs, unbounded delay, and Rosenblatt process in Hilbert spaces, using fixed point and stochastic analysis methods.

Contribution

It introduces a novel class of stochastic inclusions with Clarke's subdifferential and NIIs, providing existence results with a fixed point approach in Hilbert spaces.

Findings

Existence of solutions proved for the new class of stochastic inclusions.

Application of fixed point theorem in the context of stochastic differential inclusions.

Theoretical example demonstrating the applicability of the main results.

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.