奇异Liénard方程周期解问题

Periodic Solution of Liénard Equation with a Singularity

文章研究具奇性的Liénard微分方程x″(t)+f(x(t))x′(t)+g1(t,x(t))+g0(x(t))=p(t)的T-周期正解的存在性.利用Mawhin重合度理论和一些分析技巧,获得了方程至少存在一个T-周期正解的结果.

In this paper,the existence of positive T-periodic solutions is studied for the following singular Liénard equation x″（t）＋ f（x（t））x′（t）＋ g1（t,x（t））＋ g0（x（t））= p（t）By using Mawhin′s continuation theorem and some analysis methods,we prove that the given equation has at least one positive T-periodic solution.