On the existence and uniqueness of limit cycles in Lienard differential equations allowing discontinuities

被引：52

作者：

Llibre, Jaume ^{[1
]}

Ponce, Enrique ^{[2
]}

Torres, Francisco ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] ETS Ingenieros, Camino Descubrimientos, Seville 41092, Spain

来源：

NONLINEARITY | 2008年 / 21卷 / 09期

关键词：

D O I：

10.1088/0951-7715/21/9/013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the non-existence and the uniqueness of limit cycles for the Lienard differential equation of the form x '' - f (x) x ' + g(x) = 0 where the functions f and g satisfy xf (x) > 0 and xg(x) > 0 for x not equal 0 but can be discontinuous at x = 0. In particular, our results allow us to prove the non-existence of limit cycles under suitable assumptions, and also prove the existence and uniqueness of a limit cycle in a class of discontinuous Lienard systems which are relevant in engineering applications.

引用

页码：2121 / 2142

页数：22

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