Higher order averaging theory for finding periodic solutions via Brouwer degree
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)

Date:	2014
Abstract:	In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such differential systems, which do not need to be of class C1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338
Note:	Agraïments: The second author is partially suported by the grant FAPESP 2011/03896-0. The third author is partially supported by a FAPESP-BRAZIL grant 2007/06896-5. The first and third authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Brower degree ; Periodic solutions
Published in:	Nonlinearity, Vol. 27 (2014) , p. 563-583, ISSN 1361-6544

DOI: 10.1088/0951-7715/27/3/563

Postprint 15 p, 424.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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