Uniqueness of limit cycles for Liénard differential equations of degree four

Chengzhi Li, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

57 Citations (Scopus)

Abstract

We prove that any classical Liénard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C.C. Pugh (1977) [4] about the number of limit cycles for polynomial Liénard differential equations for n = 4. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)3142-3162
JournalJournal of Differential Equations
Volume252
Issue number4
DOIs
Publication statusPublished - 15 Feb 2012

Keywords

  • Limit cycle
  • Liénard equations

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