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

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

2007-09-29

arxiv.org/abs/0710.0057v1

Dokl. Math. Sci., 67 (2003) 36-38

Mathematics

Classical Analysis and ODEs

Appeared in Russian in Doklady of Russian Academy of Sciences, 388 (2003), no. 4, 439-442

Scientific paper

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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