扰动Van der Pol方程的周期解（英文）  

PERIODIC SOLUTIONS OF PERTURBED VAN DER POL EQUATION

作　　者：任秀芳[1] 

机构地区：[1]南京农业大学理学院数学系,南京210095

出　　处：《南京大学学报（数学半年刊）》2014年第2期125-139,共15页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by NSFC(No.11126100);the Youth Science and Technology Innovation Fund of Nanjing Agricultural University(No.KJ2010025);the Jiangsu Overseas Research&Tranning Program for University Prominent Young&Middle-aged Teachers and Presidends

摘　　要：本文证明了带小参数扰动的Van der Pol方程周期解的存在性和稳定性.主要通过构造周期函数空间上的若干算子,应用巴拿赫空间上的压缩映像原理,对线性变分方程的特征指数做分析得到结论.In this paper,we show the existence and stability of the periodic solutions of van der Pol equation with a small perturbation.The proof is based on constructing several operators in the periodic function space,applying Banach contracting-mapping principle and analyzing the characteristic exponent of the related variational equation.

关 键 词：VAN der POL方程 周期解 存在性 稳定性 

分 类 号：O175[理学—数学]