中文摘要：

本文运用Mawhin重合度拓展定理和一些分析方法研究了一类Rayleigh型p-拉普拉斯时滞平均曲率方程2kT-周期解的存在性,证明了周期解序列存在极限,且极限点就是所研究方程的同宿解.最后,我们给出例子来验证文章结论的有效性.

英文摘要：

In this paper, by applying Mawhin＇s continuation theorem, some sufficient conditions on the existence of 2kT-periodic solutions for a kind of prescribed mean curvature Rayleigh p-Laplacian equation with delays are given. Then the existence of nontrivial homoclinic solutions for prescribed mean curvature Rayleigh p-Laplacian equation with delays is obtained. At last, an example is also given to illustrate the application of our main results.