Lower bounds for the number of limit cycles of trigonometric Abel equations

被引：16

作者：

Alvarez, M. J. ^{[1
]}

Gasull, A. ^{[2
]}

Yu, J. ^{[3
]}

机构：

[1] Univ Illes Balears, Dept Math & Informat, Palma de Mallorca 07122, Spain

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

[3] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 342卷 / 01期

关键词：

Abel equation; periodic orbit; Melnikov functions;

D O I：

10.1016/j.jmaa.2007.12.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Abel equation (x) over dot = A(t)x(3) + B(t)x(2), where A(t) and B(t) are trigonometric polynomials of degree n and m, respectively, and we give lower bounds for its number of isolated periodic orbits for some values of n and m. These lower bounds are obtained by two different methods: the study of the perturbations of some Abel equations having a continuum of periodic orbits and the Hopf-type bifurcation of periodic orbits from the solution x = 0. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：682 / 693

页数：12

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