Controllability of impulsive differential inclusions with nonlocal condition driven by hemivariational inequalities

Abstract

Our motive for this study is to provide some sufficient conditions for the existence of mild solutions and approximate controllability of the semilinear impulsive differential hemivariational inequalities with a general nonlocal condition which is a nonlocal condition modeled in terms of inclusion. After that, we introduce the concept of mild solutions for the corresponding inclusion problem via taking some suitable assumptions. Then we provide a sufficient condition guaranteeing the approximate controllability of our problem and prove by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential. In this scenario, assuming that the linear system is approximately controllable, we identify three conditions that ensure the approximate controllability of the nonlinear system. Finally, we provide an application to validate our results.