Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four

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 [4] in 1977 about the number of limit cycles for polynomia...

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Detalles Bibliográficos
Autores: Li, Chengzhi, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150546
Acceso en línea:https://ddd.uab.cat/record/150546
https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002
Access Level:acceso abierto
Palabra clave:Liénard equations
Limit cycle
Descripción
Sumario: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 [4] in 1977 about the number of limit cycles for polynomial Liénard differential equations for n = 4.