Multiple periodic solutions of high order differential delay equations with 2k−1 $2k-1$ lags

Abstract

Abstract In this paper, we study the periodic solutions of high order differential delay equations with 2k−1 $2k-1$ lags. The 4k-periodic solutions are obtained by using the variational method and the method of Kaplan–Yorke coupling system. These are new types of differential delay equations compared with all previous research. And it provides a precise counting method for the number of periodic solutions. Two examples are given to demonstrate our main results.

Keywords

• High order differential delay equation
• Periodic solutions
• Critical point theory
• Variational method