On the Number of Periodic Solutions to Kaplan–Yorke-like High Order Differential Delay Equations with 2k Lags

Abstract

In this paper, we study the periodic solutions of high order differential delay equations with [Formula: see text] lags. And the [Formula: see text]-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 previous researches. And it provides a theoretical basis for the study of differential delay equations. An example is given to demonstrate our main results.

On the Number of Periodic Orbits to Odd Order Differential Delay Systems

“…They proved the existence of the periodic solutions of (1) when n = 1 and n = 2, respectively. In the subsequent literatures [4][5][6][7][8][9][10][11][12][13][14][15][16][17], the number of 2 (n + 1)-periodic solutions of Equation (1) was studied by using the results of Nussbaum [18]. In 1998, Li and He [15] made some researches for (1) by use of the theory of symmetric group.…”