Delay perturbed state-dependent sweeping process

Abstract

In this paper, we prove a result on the existence of solutions of a differential inclusion governed by a class of nonconvex state-dependent sweeping process with perturbation depending on all the variables and with delay. The moving set involved in the process is prox-regular and depends both on the time and on the state.

Keywords:

• differential inclusion
• r-prox-regular set
• subdifferential
• sweeping process

AMS Subject Classifications:

• 34A60
• 34B15
• 47H10

Acknowledgement

The authors would like to thank the anonymous referees for their valuable comments and suggestions.