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
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.
Supported by the PhD Programs Foundation of Ministry of Education of China(20070128001);the Innovation Program of Shanghai Municipal Education Commission (09YZ239);the Research Foundation of Shanghai Institute of Technology (YJ2009-12)
本文研究了Adomian分解方法在非线性分数阶微分方程求解中的应用. 利用Riemann-Liouville分数阶导数和Adomian分解方法, 将Duffing方程和Van der Pol方程联合在一个分数阶方程中,并获得了此方程的解析近似解.