Limit cycles of the generalized polynomial Liénard differential equations

Jaume Llibre, Ana Cristina Mereu, Marco Antonio Teixeira

Research output: Contribution to journalArticleResearchpeer-review

73 Citations (Scopus)


We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ + f(x)ẋ + g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m 1)/2] limit cycles, where [·] denotes the integer part function. © 2009 Cambridge Philosophical Society.
Original languageEnglish
Pages (from-to)363-383
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusPublished - 1 Mar 2010


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