Oscillation criteria for second-order nonlinear neutral difference equations of mixed type

Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. Δ 2 ( x n + a x n - τ 1 ± b x n + τ 2 ) α = q n x n - σ 1 β + p n x x + σ 2 β , n ≥ n 0 where α and β are ratio of odd positive integers with β ≥ 1. Results obtained here generalize some of the results given in the literature. Examples are provided to illustrate the main results. 2010 Mathematics Subject classification: 39A10 .