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arXiv · 1808.10123

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

Mikhail Kamenskii·Oleg Makarenkov·Lakmi Niwanthi Wadippuli
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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 $T$-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.

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Mikhail Kamenskii, Oleg Makarenkov, Lakmi Niwanthi Wadippuli. 2018-08-30. A continuation principle for periodic BV-continuous state-dependent sweeping processes. https://arxiv.org/abs/1808.10123

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