Periodic solutions of nonlinear functional difference equations at nonresonance case

Sufficient conditions for the existence of at least one T -periodic solution of nonlinear functional difference equation Δx(n)+ a(n)x(n) = f n, u(n) , is established when T−1 j=0 (1− a(j)) = 1. Here u(n) = x(n),x n −τ1(n) , . . . , x n− τm(n) , {a(n): n ∈ Z} and {τi(n): n ∈ Z}, i = 1, . . . , m, are T -periodic sequences with T 1, f (n, u) is continuous about u for each n ∈ Z and T -periodic about n for each u ∈ Rm+1. We allow f to be at most linear, superlinear or sublinear in obtained results. © 2006 Published by Elsevier Inc