Improved approach for oscillatory solutions of second order half-linear neutral delay difference equations

We establish the oscillatory solutions of a second order half-linear neutral delay difference equations of the form Δ(an(Δzn)α)+qnxn−1α=0 for n ≥ n0 > 0, N(n0) = { n0, n0 + 1, … } n0 is a non negative integer and α is ratio of odd positive integers. Where zn=xn−ρnxn−m for all n ∈ N(n0), with the condition ∑s=n0∞as−1α=∞. By using the classical Riccati transformation techniques, we present new oscillation criteria of studied equations and examples are provided to illustrate the main results.