Improving the averaging theory for computing periodic solutions of the differential equations
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	For m = 1, 2, 3, we consider differential systems of the form x0 = F0(t, x) +Xmi=1εiFi(t, x) + εm+1R(t, x, ε), where Fi: R × D → Rn, and R : R × D × (−ε0, ε0) → Rn are Cm+1 functions, and T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such system we assume that the unperturbed system x0 = F0(t, x) has a k-dimensional manifold of periodic solutions with k ≤ n. We weaken the sufficient assumptions for studying the periodic solutions of the perturbed system when (ε) > 0 is sufficiently small.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2013/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB-10-4E-378. The second author is partially supported by a FAPESP-BRAZIL grant 2013/16492-0. The two authors are also supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Limit cycles ; Lyapunov-Schmidt reduction ; Nonlinear differential systems ; Periodic solutions
Published in:	ZAMP. Journal of Applied Mathematics and Physics, Vol. 66 Núm. 4 (2014) , p. 1401-1412, ISSN 1420-9039

DOI: 10.1007/s00033-014-0460-3

Postprint 16 p, 329.9 KB

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