A new approach in the theory of ordinary differential equations with small parameter
Classical Analysis and ODEs
2007-10-02 v1
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.
Keywords
Cite
@article{arxiv.0710.0057,
title = {A new approach in the theory of ordinary differential equations with small parameter},
author = {Mikhail Kamenskii and Oleg Makarenkov and Paolo Nistri},
journal= {arXiv preprint arXiv:0710.0057},
year = {2007}
}
Comments
Appeared in Russian in Doklady of Russian Academy of Sciences, 388 (2003), no. 4, 439-442