The oscillation/nonoscillation of nonlinear difference equations

In this paper, we establish new criteria for the oscillation/nonoscillation of solutions of the nonlinear difference equation of the form ∇ (rnΦ(Δyn)) + qnΦ(yn) = Rn, where Φ :→ R is defined by Φ(s) = |s|P−1 s, p > 0 a fixed real number, and a Hille-Wintner type comparison theorem is established.