THE NUMBER OF LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS WITH PERIODIC COEFFICIENTS OF DEFINITE SIGN

被引：19
|
作者：
Alvarez, Amelia [1 ]
Bravo, Jose-Luis [1 ]
Fernandez, Manuel [1 ]
机构：
[1] Univ Extremadura, Dept Matemat, E-06071 Badajoz, Spain
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 05期
关键词：
Abel equation; periodic solution; limit cycle;
D O I：
10.3934/cpaa.2009.8.1493
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the number of limit cycles (isolated periodic solutions in the set of all periodic solutions) for the generalized Abel equation x' = a(t)x(n)a+b(t)x(n)b+c(t)x(n)c+d(t)x, where n(a) > n(b) > n(c) > 1, a(t), b(t), c(t), d(t) are 2 pi-periodic continuous functions, and two of a(t), b(t), c(t) have definite sign. We obtain examples with at least seven limit cycles, and some sufficient conditions for the equation to have at most one or at most two positive limit cycles.
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页码：1493 / 1501
页数：9
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