Báo Cáo Báo cáo hóa học PERIODIC SOLUTIONS FOR A COUPLED PAIR OF DELAY DIFFERENCE EQUATIONS GUANG ZHANG, SHU

ERIODIC SOLUTIONS FOR A COUPLED PAIR OF DELAY DIFFERENCE EQUATIONS GUANG ZHANG, SHUGUI KANG, AND SUI SUN CHENG Received 31 January 2005 and in revised form 24 March 2005

Based on the fixed-point index theory for a Banach space, positive periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions for delay difference equations with positive and negative terms is also considered.

1. Introduction The existence of positive periodic solutions for delay difference equations of the form xn+1 = an xn + hn f n,xnưτ(n) , n ∈ Z = { ., ư2, ư1,0,1,2, .}, (1.1) has been studied by many authors, see, for example, [1, 3, 5, 7, 8, 9] and the references contained therein. The above equation may be regarded as a mathematical model for a number of dynamical processes. In particular, xn may represent the size of a population in the time period n. Since it is possible that the population may be influenced