Existence and uniqueness of limit cycles for generalized φ-Laplacian Lienard equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:439

Article

Perez-Gonzalez, S.¹  Torregrosa, J.²  Torres, P. J.³ 

[1] Univ Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[2] Univ Autonoma Barcelona, Dept Matemat, Edifici C, E-08193 Barcelona, Spain

[3] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

关键词: Existence and uniqueness;    Periodic orbits;    Limit cycles;    phi-Laplacian Lienard equations;    Generalized Lienard. equations;   

DOI  :  10.1016/j.jmaa.2016.03.004

来源: Elsevier

【 摘 要 】

The Lienard 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 Lienard equations. In this paper we extend some of these results for the case of the generalized phi-Laplacian Lienard equation, (phi(x'))' f(x)psi(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'/root 1 - (x'/c)(2))' + mu(x(2) - 1)x' + x = 0, has a unique periodic orbit when mu = 0. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free