一类具有排斥型奇性的中立型Linard方程周期正解的存在性

Existence of Positive Periodic Solutions for Neutral Linard Equations with a Singularity of Repulsive Type

利用Mawhin重合度拓展定理,研究一类具有排斥型奇性的中立型Linard方程周期问题.在强奇性条件下,获得周期正解存在性的新结果.本文允许方程在无穷远点具有不定型奇性,改进了已有文献中的相关结论.

By using Mawhin＇s continuation theorem, the problem of periodic solutions is studied for neutral Liénard equation with a singularity of repulsive type. Under the strong singularity condition,a new result on the existence of positive periodic solutions is obtained. It＇s interesting that is that the singularity at infinity is allowed indefinite type, which generalizes the corresponding results in known literature.