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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139015A 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.Appeared in Russian in Doklady of Russian Academy of Sciences, 388 (2003), no. 4, 439-442Classical Analysis and ODEs54C40; 14E20; 46E25; 20C20A new approach in the theory of ordinary differential equations with small parametertext