符号(数学)
极限(数学)
数学
数学分析
物理
数学物理
组合数学
作者
Amelia Álvarez,José-Luis Bravo,Manuel Montanero Fernández
出处
期刊:Communications on Pure and Applied Analysis
[American Institute of Mathematical Sciences]
日期:2009-04-01
卷期号:8 (5): 1493-1501
被引量:18
标识
DOI:10.3934/cpaa.2009.8.1493
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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