# Article

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Keywords:
oscillatory solutions; difference equations
Summary:
We offer sufficient conditions for the oscillation of all solutions of the perturbed difference equation $$|\Delta^{m} y(k)|^{\alpha-1}\Delta^{m} y(k)+Q(k,y(k-\sigma_{k}), \Delta y(k-\sigma_{k}),\cdots, \Delta^{m-2}y(k-\sigma_{k}))$$ \hfill $=P(k,y(k-\sigma_{k}),\Delta y(k-\sigma_{k}),\cdots, \Delta^{m-1}y(k-\sigma_{k})),~k\geq k_{0}$ where $\alpha>0.$ Examples which dwell upon the importance of our results are also included.
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