Existence and uniqueness of limit cycles for generalized -Laplacian Liénard equations

The Liénard equation x'' + f(x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Li'enard equations. In this paper we...

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Detalles Bibliográficos
Autores: Pérez-González, Set|||0000-0002-1522-7086, Torregrosa, Joan|||0000-0002-2753-1827, Torres, Pedro J.
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169444
Acceso en línea:https://ddd.uab.cat/record/169444
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.03.004
Access Level:acceso abierto
Palabra clave:Existence and Uniqueness
Generalized Liénard equations
Limit cycles
Periodic orbits
φ-Laplacian Liénard equations
Descripción
Sumario:The Liénard equation x'' + f(x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Li'enard equations. In this paper we extend some of these results for the case of the generalized ϕ-Laplacian Liénard equation, (ϕ(x'))' + f(x)ψ(x') + g(x) = 0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, [x'/p1 - (x'/c)2]'+ µ(x2 - 1)x' + x = 0, has a unique periodic orbit when µ 6= 0.