Periodic solutions of some classes of continuous second-order differential equations

Jaume Llibre, Amar Makhlouf

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

We study the periodic solutions of the second-order differential equations of the form ẍ ± xn = μ f (t), or ẍ ± |x|n = μ f(t), where n = 4, 5,⋯, f(t) is a continuous T-periodic function such that ∫ 0T f(t)dt = 0, and μ is a positive small parameter. Note that the differential equations ẍ ± xn = μ f(t) are only continuous in t and smooth in x, and that the differential equations ẍ ± |x|n = μ f(t) are only continuous in t and locally-Lipschitz in x.
Original languageEnglish
Pages (from-to)477-482
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number2
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • Averaging theory
  • Periodic solution
  • Second order differential equations

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