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

Abstract

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.

COMMUNICATED BY:

• D. Motreanu

Keywords:

• Approximate controllability
• second-order systems
• hemivariational inequality
• Clarke subdifferential
• cosine function of operators

2010 Mathematics Subject Classifications:

• 39B05
• 49J53

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is supported by NNSF of China [grant numbers 12071413 and 11961074], NSF of Guangxi [grant numbers 2018GXNSFDA138002, 2020GXNSFAA159052]. This project has also received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731-CONMECH.