Uniqueness of limit cycles for Liénard differential equations of degree four

Chengzhi Li; Jaume Llibre

doi:10.1016/j.jde.2011.11.002

Uniqueness of limit cycles for Liénard differential equations of degree four

Chengzhi Li, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

53 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 language	English
Pages (from-to)	3142-3162
Journal	Journal of Differential Equations
Volume	252
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2011.11.002
Publication status	Published - 15 Feb 2012

Keywords

Liénard equations
Limit cycle

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title = "Uniqueness of limit cycles for Li{\'e}nard differential equations of degree four",

abstract = "We prove that any classical Li{\'e}nard 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 Li{\'e}nard differential equations for n = 4. {\textcopyright} 2011 Elsevier Inc.",

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AU - Li, Chengzhi

AU - Llibre, Jaume

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N2 - 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.

AB - 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.

KW - Liénard equations

KW - Limit cycle

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DO - 10.1016/j.jde.2011.11.002

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VL - 252

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EP - 3162

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