Nonoscillatory solutions for the one-dimensional p-Laplacian

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