In this paper, we establish new criteria for the oscillation/nonoscillation of solutions of the nonlinear difference equation of the form del (r(n) Phi (Delta y(n))) + q(n) Phi(y(n)) = R-n, where Phi :--> R is defined by Phi(s) = \s\(p-1)s, p > 0 a fixed real number, and a Hille-Wintner type comparison theorem is established. (C) 2000 El...