一类具多时滞二阶非线性微分方程的周期解

Periodic Solutions for Second-Order Differential Equations with Deviating Arguments

研究一类具有多变时滞的二阶非线性微分方程x″(t)+f1(x(t))x′(t)+f2(x(t-τ1(t)))(x′(t))2+g(t,x(t-τ2(t)))的周期解的存在性问题.利用重合度理论中的连续定理和一些分析技巧,得到该方程存在周期解的一些新结果,所得结果推广和改进了刘斌的结果.

In this paper,we study the problem on the existence of periodic solutions for a class of nonlinear second-order differential equations with deviating arguments x″（t）＋f1（x（t））x′（t）＋f2（x（t-τ1（t）））（x′（t））2＋g（t,x（t-τ2（t）））.By means of the continuation theorem of coincidence degree theory and some analysis techniques,we obtain some news results on the existence of periodic solutions for the equations.Our results generalize and improve the one made by Liu Bin.