  In the setting adopted by Edmond and Thibault [Mathematical Programming 104
(2005), 347--373], we study a class of perturbed sweeping processes. Under
suitable assumptions, we obtain two solution existence theorems for perturbed
sweeping processes with the constraint sets being prox-regular sublevel sets.
The results are applied to analyzing the behavior of some concrete mechanical
sweeping processes, which appear for the first time in this paper.
