Periodic solutions and their stability of some higher-order positively homogenous differential equations

Xiuli Cen, Jaume Llibre, Meirong Zhang

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2017 Elsevier Ltd In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1, h(t) is a continuous T-periodic function of non-zero average, and μ is a positive small parameter. By using the averaging theory, we will give the existence of T-periodic solutions. Moreover, the instability and the linear stability of these periodic solutions will be obtained.
Original languageEnglish
Pages (from-to)285-288
JournalChaos, Solitons and Fractals
Volume106
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Averaging theory
  • Periodic solution
  • Stability
  • m-Order differential equations

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