Lu Shiping
College of Math & Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044 China.
J Inequal Appl. 2017;2017(1):37. doi: 10.1186/s13660-016-1285-8. Epub 2017 Feb 7.
In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text], and are -periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function [Formula: see text] is allowed to change for [Formula: see text].
本文研究了具有排斥型奇点的二阶微分方程[y''(t)+a(t)y'(t)+b(t)y^{\alpha}(t)=e(t)]的周期解的存在性问题，其中(b(t))在(t = 0)处奇异，(a(t))、(b(t))和(e(t))是(\omega -)周期函数。通过使用马纳塞维奇和马欣的连续定理，得到了关于正周期解存在性的一个新结果。有趣的是，允许函数(b(t))的符号在(t\in[0,\omega])内发生变化。
