A new approach in the theory of ordinary differential equations with small parameter

Mikhail Kamenskii; Oleg Makarenkov; Paolo Nistri

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arXiv · 0710.0057

A new approach in the theory of ordinary differential equations with small parameter

Mikhail Kamenskii·Oleg Makarenkov·Paolo Nistri

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Abstract

A topological degree based averaging principle has been proposed by J. Mawhin in his PhD thesis [J. Mawhin, Le Probleme des Solutions Periodiques en Mecanique non Lineaire, These de doctorat en sciences, Universite de Liege, 1969]. In the present paper we extend this result for the case when the unperturbed system is nonlinear but possesses a set of T-periodic solutions whose initial conditions constitute a boundary of some open set.

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Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri. 2007-09-29. A new approach in the theory of ordinary differential equations with small parameter. https://arxiv.org/abs/0710.0057

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