A measure differential inclusion involving time-dependent maximal monotone operators

TL;DR

This paper proves the existence and uniqueness of solutions with specific regularity for a differential inclusion involving time-dependent maximal monotone operators, advancing the mathematical understanding of such systems.

Contribution

It introduces a new existence and uniqueness result for solutions to perturbed differential inclusions with time-dependent maximal monotone operators.

Findings

Established existence of right continuous solutions with bounded variation

Proved uniqueness of solutions under given conditions

Extended the theory of differential inclusions with time-dependent operators

Abstract

We establish in this paper, an existence and uniqueness result of right continuous with bounded variation solution for a perturbed differential inclusion governed by time-dependent maximal monotone operators.