Periodic solutions of Lienard differential equations via averaging theory of order two

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

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2015 Academia Brasileira de Ciencias. All rights reserved. For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form (formula presented) where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
Original languageEnglish
Pages (from-to)1905-1913
JournalAnais da Academia Brasileira de Ciencias
Volume87
Issue number4
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • Averaging theory
  • Bifurcation theory
  • Lienard differential equation
  • Periodic solution

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