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Periodic Solutions for a Class of Singulary Perturbated Systems by Kamenskii, Mikhail; Makarenkov, Oleg; Nistri, Paolo is a scholarly article available to read on EtoBox.

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In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here $e>0$ is the perturbation parameter. Our approach, based on the topological degree theory and the averaging theory, permits to weaken the conditions in [K.R. Schneider, Vibrational control of singularly perturbed systems, in "Lectures Notes in Control and Information Science", 259, 397-408, Springer, London, 2001, Theorem 2] under which the existence of periodic solutions is proved.

Author

Kamenskii, Mikhail; Makarenkov, Oleg; Nistri, Paolo

Published

2007

Language

EN