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Limit cycles of the generalized polynomial Liénard differential equations

Published online by Cambridge University Press:  12 November 2009

JAUME LLIBRE ,
ANA CRISTINA MEREU  and
MARCO ANTONIO TEIXEIRA
JAUME LLIBRE
Affiliation:
Departament de Matemtiques, Universitat Autnoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain. e-mail: jllibre@mat.uab.cat
ANA CRISTINA MEREU
Affiliation:
Departamento de Matemtica, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, S.P, Brazil. e-mail: anameren@ime.unicamp.br, teixeira@ime.unicamp.br
MARCO ANTONIO TEIXEIRA
Affiliation:
Departamento de Matemtica, Universidade Estadual de Campinas, Caixa Postal 6065, 13083-970, Campinas, S.P, Brazil. e-mail: anameren@ime.unicamp.br, teixeira@ime.unicamp.br
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 2 , March 2010 , pp. 363 - 383
Copyright
Copyright © Cambridge Philosophical Society 2009

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