中文摘要：

应用变分方法与无穷维空间Morse理论研究方程x=g（x（t-r））,得到上述微分差分方程以4r为周期的非常数周期解存在性的条件,并且给出其个数的下界.因此为研究含有时滞的微分系统周期解的存在性提供了一种新方法.

英文摘要：

In this paper, by using variational methods and infinite dimensional Morse theory, a sufficient condition is obtained for the existence of multiple nontrivial 4r-periodic solutions to the following delay differential equations x=g（x（t-r））.A lower bound of the number of periodic solutions is also given. As a consequence of this paper, a new method is introduced for investigating the periodic solutions of delay differential equations.