中文摘要：

本文利用不动点定理,重合度理论和一些新的分析方法研究了一类时滞微分方程x″（t）＋a[x′（t）]m＋bx（t-τ）=f（t）,m∈Z＋周期解的存在性,得到了周期解存在性的新结论.值得注意的是本文所使用的方法与以往文章均不相同.

英文摘要：

By using the continuation theorem of coincidence degree theory, fixed point theorems and some new analysis skill, the authors study the existence of periodic solution to a kind of second-order differential equation with a deviating argument x″（t）＋a[x′（t）]m＋bx（t-τ）=f（t）,m∈Z＋ Some new results on the existence of periodic solution is obtained. Furthermore, the significance of this paper is that the methods to this paper are different from the corresponding ones used in the past.