A continuation principle for periodic BV-continuous state-dependent sweeping processes
Dynamical Systems
2018-10-18 v2
Abstract
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 processes). By setting up an appropriate catching-up algorithm we prove solvability of the initial value problem. Then, for sweeping processes with -periodic right-hand-sides, we prove the existence of at least one -periodic solution. Finally, we further consider a -periodic sweeping process which is close to an autonomous sweeping process with a constant constraint and prove the existence of a -periodic solution specifically located near the boundary switched equilibrium of the autonomous sweeping process.
Cite
@article{arxiv.1808.10123,
title = {A continuation principle for periodic BV-continuous state-dependent sweeping processes},
author = {Mikhail Kamenskii and Oleg Makarenkov and Lakmi Niwanthi Wadippuli},
journal= {arXiv preprint arXiv:1808.10123},
year = {2018}
}