A Continuation Principle for Periodic BV-Continuous State-Dependent Sweeping Processes
Mikhail Kamenskiĭ, Oleg Makarenkov, Lakmi Niwanthi Wadippuli · SIAM Journal on Mathematical Analysis · 2020
We consider a Caratheodory differential equation with a state-dependent convex constraint that changes BV-continuously in time (a perturbed BV-continuous state-dependent sweeping process). 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 investigate 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.