Periodic solutions of nonlinear periodic differential systems with a small parameter

Adriana Buicǎ, Jean Pierre Françoise, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

102 Citations (Scopus)

Abstract

We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide sufficient conditions in order that some of the periodic orbits of this invariant manifold persist after the perturbation. These conditions are not difficult to check, as we show in some applications. The key tool for proving the main result is the Lyapunov-Schmidt reduction method applied to the Poincaré-Andronov mapping.
Original languageEnglish
Pages (from-to)103-111
JournalCommunications on Pure and Applied Analysis
Volume6
Issue number1
Publication statusPublished - 1 Jan 2007

Keywords

  • Averaging method
  • Lyapunov-Schmidt reduction
  • Periodic solution

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