Existence and uniqueness of limit cycles for generalized -Laplacian Liénard equations
Pérez-González, Set (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torres, Pedro J. (Universidad de Granada. Departamento de Matemática Aplicada)

Date:	2016
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad UNAB13-4E-1604 Ministerio de Economía y Competitividad MTM2014-52232-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
Note:	Agraïments: The first author is also supported by a PNPD/CAPES grant. The third author is supported by FQM-1861 (Junta de Andalucía) grants.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Existence and Uniqueness ; Generalized Liénard equations ; Limit cycles ; Periodic orbits ; φ-Laplacian Liénard equations
Published in:	Journal of mathematical analysis and applications, Vol. 439 (2016) , p. 745-765, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2016.03.004

Postprint 21 p, 458.8 KB

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