Constant-sign periodic and almost periodic solutions of a system of difference equations

We consider the following system of difference equations, u(i) (k) = Sigma(e is an element of Z) gi (k, l) f (l u(1) (l), u(2) (l),...,u(2) (l)), k is an element of I, 1 <= i <= n, where I is a subset of Z. Our aim is to establish criteria such that the above system has a constant-sign periodic and almost periodic solution (u(1), u(2),...,u(n).). The above problem is also extended to that on u(1) (k) = Sigma(e is an element of Z) g(i) (k, l) fi (l, u(1) (l), u(2) (l),..., u(n), k is an element of Z, 1 <= i <= n. (c) 2005 Elsevier Ltd. All rights reserved.