中文摘要：

本文研究了如下Rayleigh型时滞平均曲率方程（u′（t）/√1＋（u′（t））^2）′＋f（t,u′（t））＋g（u（t-τ（t）））=p（t）周期解的存在性问题.运用Mawhin重合度扩展定理,本文给出了证明方程至少存在一个T-周期解的充分性条件.最后本文给出例子验证了文章的主要结论.

英文摘要：

In this paper, we give certain sufficient conditions for the existence of periodic solutions to the following prescribed mean curvature Rayleigh equations with a deviating argument （u′（t）/√1＋（u′（t））^2）′＋f（t,u′（t））＋g（u（t-τ（t）））=p（t）By using Mawhin＇s continuation theorem, we prove that the given equation has at least one T- periodic solution. At last, we give an example to illustrate the application of our main results.