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Pàgina inicial > Articles > Articles publicats > Improving the averaging theory for computing periodic solutions of the differential equations |
Data: | 2014 |
Resum: | 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. |
Ajuts: | 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 |
Nota: | 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. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Averaging theory ; Limit cycles ; Lyapunov-Schmidt reduction ; Nonlinear differential systems ; Periodic solutions |
Publicat a: | ZAMP. Journal of Applied Mathematics and Physics, Vol. 66 Núm. 4 (2014) , p. 1401-1412, ISSN 1420-9039 |
Postprint 16 p, 329.9 KB |