Constant-Sign Periodic and Almost Periodic Solutions of a System of Difference Equations

摘要

We consider the following system of difference equations, u_i (k) = ∑_(l ∈I) g_i (k, l) f (l, u_1 (l), u_2 (l), …, u_n (l)), k ∈ 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 Z, u_i (k) = ∑_(l ∈Z) g_i (k, l) f_i (l, u_1 (l), u_2 (l), …, u_n (l)), k ∈ Z, 1 ≤ i ≤ n,