Higher order averaging theory for finding periodic solutions via Brouwer degree

Jaume Llibre, Douglas D. Novaes, Marco A. Teixeira

Research output: Contribution to journalArticleResearchpeer-review

62 Citations (Scopus)

Abstract

In this paper we deal with nonlinear differential systems of the form x'(t) = Σki=0 εiFi (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, and T -periodic in the first variable, D being 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. © 2014 IOP Publishing Ltd.
Original languageEnglish
Pages (from-to)563-583
JournalNonlinearity
Volume27
Issue number3
DOIs
Publication statusPublished - 1 Mar 2014

Keywords

  • averaging method
  • Brouwer degree
  • discontinuous differential system
  • non-smooth differential system
  • periodic solution

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