A continuation principle for periodic BV-continuous state-dependent sweeping processes

Abstract

We consider a Caratheodory differential equation with a state-dependent convex constraint that changes BV-continuously in time (a perturbed BVcontinuous state-dependent sweeping processes). By setting up an appropriate catching-up algorithm we prove solvability of the initial value problem. Then, for sweeping processes with T -periodic right-hand-sides, we prove the existence of at least one T -periodic solution. Finally, we further consider a T -periodic sweeping process which is close to an autonomous sweeping process with a constant constraint and prove the existence of a T -periodic solution specifically located near the boundary switched equilibrium of the autonomous sweeping process.