In this paper, we study the periodic solutions to a type of differential delay equations with 2k − 1 lags. The 4k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system. This is a new type of differential delay equations compared with all the previous researches. And this paper provides a theoretical basis for the study of differential delay equations. An example is given to demonstrate our main results.

中文翻译：

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具有 2k − 1 个滞后的微分延迟方程的多重周期解

在本文中，我们研究了一类滞后时间为 2k − 1 的微分延迟方程的周期解。利用变分法和Kaplan-Yorke耦合系统的方法获得了4k周期解。与以往的所有研究相比，这是一种新型的微分延迟方程。为微分时滞方程的研究提供了理论依据。给出了一个例子来证明我们的主要结果。