Asymptotic behavior of Positive Solutions of Second-Order Nonlinear Difference Systems.

In this paper, several necessary and/or sufficient conditions are given for the asymptotic behavior of positive solutions of second-order nonlinear difference systems of the form {Δ(r1(n)Δu1(n)) + f1(n, u2(n - τ2)) = 0 Δ(r2(n)Δu2(n)) + f2(n, u1 (n τ1)) 0, ∈ N(n0), where N(n0) = {n0, n0 + 1, n0 + 2, ...}(n0 is a fixed nonnegative integer), ri(n) > 0 for n ≥ n0 such that Σ∞ 1\ri (n) = ∞, and fi : N(n0) x R → R is a real-valued increasing and continuous function in x such that f(n, x) ≥ 0 for all (n, x) ∈ N(n0) x (0, ∞), τi is positive constant (i = 1, 2). [ABSTRACT FROM AUTHOR]