Properties of solutions of higher order difference equations

This paper is concerned with the study of asymptotic behavior of solutions of the nonlinear difference equation Δm[u(n) + p(n)u(n − k)] = q(n)f(u(τ(n))), m ≥ 1, n ϵ N, where δm is the mth-order forward difference operator p : N → R, q : N → [0, ∞), τ : N → Z, k is a positive integer, f : R → R, uf(u) > 0 for u ≠ 0.