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

Departament de Matemàtiques

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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.

Idioma original	Anglès
Pàgines (de-a)	3142-3162
Revista	Journal of Differential Equations
Volum	252
Número	4
DOIs	https://doi.org/10.1016/j.jde.2011.11.002
Estat de la publicació	Publicada - 15 de febr. 2012

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10.1016/j.jde.2011.11.002

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

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https://www.scopus.com/pages/publications/84455202373

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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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author = "Chengzhi Li and Jaume Llibre",

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journal = "Journal of Differential Equations",

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TY - JOUR

T1 - Uniqueness of limit cycles for Liénard differential equations of degree four

AU - Li, Chengzhi

AU - Llibre, Jaume

PY - 2012/2/15

Y1 - 2012/2/15

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

UR - https://www.scopus.com/pages/publications/84455202373

U2 - 10.1016/j.jde.2011.11.002

DO - 10.1016/j.jde.2011.11.002

M3 - Article

SN - 0022-0396

VL - 252

SP - 3142

EP - 3162

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

Uniqueness of limit cycles for Liénard differential equations of degree four

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