Limit Cycles for Generalized Abel Equations
Limit Cycles for Generalized Abel Equations
复制标题
DOI：
10.1142/s0218127406017130
复制
发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
A. Gasull;A. Guillamón
中科院分区：
文献类型：
--
作者：
A. Gasull;A. Guillamón
本文研究了一类一维非自治微分方程的周期解的个数上界问题，这类方程的右边为n次多项式，其系数为实光滑单周期函数。n = 3的情况给出了所谓的阿贝尔方程，这个方程已经被彻底地研究过了，而且很容易理解。我们考虑阿贝尔方程的两种自然推广。我们的结果扩展了Lins Neto和Panov之前的工作，并试图在理解b>3的情况下向前迈进一步。它们也可用于控制某些平面常微分方程的极限环数。
This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional nonautonomous differential equations: those with the right-hand sides being polynomials of degree n and whose coefficients are real smooth one-periodic functions. The case n = 3 gives the so-called Abel equations which have been thoroughly studied and are well understood. We consider two natural generalizations of Abel equations. Our results extend previous works of Lins Neto and Panov and try to step forward in the understanding of the case n > 3. They can be applied, as well, to control the number of limit cycles of some planar ordinary differential equations.