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.