Periodic orbits for perturbed non-autonomous differential equations

B. Coll, A. Gasull, R. Prohens

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We consider non-autonomous differential equations, on the cylinder (t,r)∈S 1×R{double-struck} d, given by dr/dt=f(t, r, ε) and having an open continuum of periodic solutions when ε = 0. From the study of the variational equations of low order we obtain successive functions such that the simple zeroes of the first one that is not identically zero control the periodic orbits that persist for the unperturbed equation. We apply these results to several families of differential equations with d=1, 2, 3. They include some autonomous polynomial differential equations and some Abel type non-autonomous differential equations. © 2012 Elsevier Masson SAS.
Original languageEnglish
Pages (from-to)803-819
JournalBulletin des Sciences Mathematiques
Volume136
Issue number7
DOIs
Publication statusPublished - 1 Oct 2012

Keywords

  • Bifurcation
  • Limit cycle
  • Periodic orbit
  • Variational equation

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