Uniqueness of limit cycles for Liénard differential equations of degree four

Chengzhi Li; Jaume Llibre

doi:https://doi.org/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

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 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

Limit cycle
Liénard equations

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https://doi.org/10.1016/j.jde.2011.11.002

https://ddd.uab.cat/record/150546

Cite this

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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 - Limit cycle

KW - Liénard equations

U2 - https://doi.org/10.1016/j.jde.2011.11.002

DO - https://doi.org/10.1016/j.jde.2011.11.002

M3 - Article

VL - 252

SP - 3142

EP - 3162

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 4

ER -

Uniqueness of limit cycles for Liénard differential equations of degree four

Abstract

Keywords

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