Multiple Periodic Solutions of Differential Delay Equations with 2k − 1 Lags

In this paper, we study the periodic solutions to a type of differential delay equations with 2 k − 1 lags. The 4 k -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.