Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Periodic solutions of higher-dimensional discrete systems

Zhan Zhoua1, Jianshe Yua1 and Zhiming Guoa1

a1 Department of Applied Mathematics, Guangzhou University, Guangzhou, Guangdong 510405, People's Republic of China

Abstract

Consider the second-order discrete system

S0308210500003607disp001

where f xs2208 C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) xs2208 R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

(Received August 06 2003)

(Accepted April 21 2004)