Paper

Higher order averaging theory for finding periodic solutions via Brouwer degree

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Published 25 February 2014 • © 2014 IOP Publishing Ltd & London Mathematical Society
, , Citation Jaume Llibre et al 2014 Nonlinearity 27 563 DOI 10.1088/0951-7715/27/3/563

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This article is corrected by 2014 Nonlinearity 27 2417

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Author e-mails

jllibre@mat.uab.cat

ddnovaes@mat.uab.cat

ddnovaes@ime.unicamp.br

teixeira@ime.unicamp.br

Author affiliations

1 Departament de Matematiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

2 Departamento de Matematica, Universidade Estadual de Campinas, Rua Srgio Buarque de Holanda, 651, Cidade Universitria Zeferino Vaz, 13083-859, Campinas, SP, Brazil

Dates

  1. Received 6 March 2013
  2. Accepted 20 January 2014
  3. Published

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0951-7715/27/3/563

Abstract

In this paper we deal with nonlinear differential systems of the form

where $F_i:\mathbb{R}\times D\rightarrow\mathbb{R}^n$ for i = 0, 1, ..., k, and $R:\mathbb{R}\times D\times(-\varepsilon_0,\varepsilon_0)\rightarrow\mathbb{R}^n$ are continuous functions, and T-periodic in the first variable, D being an open subset of $\mathbb{R}^n$ , and ε a small parameter. For such differential systems, which do not need to be of class $\mathcal{C}^1$ , under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed.

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10.1088/0951-7715/27/3/563