Bulletin of the Australian Mathematical Society

Research Article

Periodic solutions of some differential delay equations created by Hamiltonian systems

Jibin Lia1, Zhengrong Liua2 and Xuezhong Hea3

a1 Kunming University of Science and Technology Institute of Applied Mathematics of Yunnan Province Kunming, 650093 Peoples Rrepublic of China

a2 Department of Mathematics Yunnan University Institute of Applied Mathematics of Yunnan Province Kunming, 650091 Peoples Republic of China

a3 School of Mathematics and Statistics The University of Sydney Sydney, NSW 2006 Australia

Abstract

This paper is concerned with finding periodic solutions of differential delay systems

S000497270003656X_eqnU1

and

S000497270003656X_eqnU2

where ri (i = 1, 2,…, n − 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.

(Received February 04 1999)