Non Oscillation of Second Order Non Linear Neutral Delay Difference Equations

In the paper, we investigate the oscillatory and non-oscillatory behavior of solutions of second order non-linear neutral delay difference equations of the form ( ) ( ( ) ( ) ( ( ))) ( ( ) ( ) ( ( ))) ( ( ( ))) 1 a n x n p n x n x n p n x n f n, x n 0 a t t s _ − _ D_ D + D + _+ = _ _ where a > 0 is a constant, a(n),q(n), p(n) are positive sequences. Some examples are provided to illustrate the results obtained in this paper.