Approximate controllability of non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions

The goal of this paper is to deal with approximate controllability of control systems described by non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions in Hilbert spaces. First we define the concept of mild solution relying on the existence of an evolution operator for the corresponding linear equation and the property of Clarke subdifferential. Next, the solvability and approximate controllability are considered by means of a fixed-point strategy. Finally, two examples are provided to illustrate our main results.

Automated summary

This paper aims to address the approximate controllability of control systems described by non-autonomous second-order evolution hemivariational inequalities with nonlocal conditions in Hilbert spaces. A concept of mild solution is first defined based on the existence of an evolution operator for the corresponding linear equation and the property of Clarke subdifferential. Then, the solvability and approximate controllability are investigated using a fixed-point strategy. Finally, two examples are provided to illustrate the main results.