Oscillation criteria for second-order nonlinear difference equations with damped term

Several oscillation criteria are established for the second-order damped nonlinear difference equation Δ[an −1(Δyn −1)θ] + pn−1(Δyn−1)θ + qnƒ(yn) = 0, n n0 > 0, where θ > 0 is any quotient of odd integers, pn and qn are real sequences, and f C(R, R) such that x f (x) > 0 for x ≠ 0. Several examples which dwell upon the importance of our results are also included.