一维周期方程的周期解问题

Periodic solutions of one dimensional T-periodic differential equations

本文给出研究一维周期微分方程周期解的若干方法,包括利用Poincaré映射来判定周期解的个数、零解的稳定性及其重数、规范形方法和平均法等,其中既有对已有结论的总结和改进,又包含了一些新的结论.

In this paper, we give several methods to study periodic solutions of one dimensional T-periodic differential equations, including Poincare map, the stability of zero and its multiplicity, normal form and averaging method. Here, we summarize and improve some existing results, and state our new conclusion as well.