On perturbed sweeping process

Abstract

This paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition and a scalarly upper semicontinuous set-valued map.

Keywords:

• Lipschitz map
• r-prox-regularity
• set-valued map
• sweeping process

AMS Subject Classifications:

• 34A60
• 28A25
• 28C20