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neutral delay; difference equation; oscillation
Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation \[ \Delta (c_n\Delta (y_n+p_ny_{n-k}))+q_ny_{n+1-m}^\beta =0,\quad n\ge n_0 \] where $k$, $m$ are positive integers and $\beta $ is a ratio of odd positive integers are established, under the condition $\sum _{n=n_0}^{\infty }\frac{1}{c_n}<{\infty }.$
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