# Article

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Keywords:
third order neutral difference equation; oscillation; nonoscillation
Summary:
Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form \begin {equation*} \Delta (a_n(\Delta ^2(x_n+b_{n}x_{n-\delta }))^\alpha )+q_{n}x^{\alpha }_{n+1-\tau }=0 \end {equation*} and \begin {equation*} \Delta (a_n(\Delta ^2(x_n-b_nx_{n-\delta }))^\alpha )+q_nx^{\alpha }_{n+1-\tau }=0 \end {equation*} are established. Some examples are presented to illustrate the main results.
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