In this paper we study the existence of nonoscillatory solutions of the equation ΔΦ(Δx_k−1) + f(k,x_k) = 0, k = 1,2,…, where is defined by Φ(s) = ¦s¦^p−2s with p> 1, and {x_k}₁^∞ is a nonnegative sequence with infinitely many positive terms.