Abstract

We study the existence and uniqueness of solutions to a differential sweeping system. This system is an implicit coupled dynamical system consisting of a nonlinear differential equation and a history/state-dependent sweeping process. First, an existence result to a perturbed state-dependent sweeping process is proved based on Schauder's fixed-point theorem. Next, the unique solvability of a history/state-dependent sweeping process is established by employing a fixed-point theorem for a history-dependent operator. Finally, using tools from nonsmooth analysis and Banach's fixed-point theorem, we establish the existence and uniqueness of solutions to a differential sweeping system.