Geodesic
The oscillation of an $m$th order perturbed nonlinear difference equation
Archivum mathematicum, Tome 32 (1996) no. 1, pp. 13-27.

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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.
Classification : 39A10
Keywords: oscillatory solutions; difference equations 
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     title = {The oscillation of an $m$th order perturbed nonlinear difference equation},
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     pages = {13--27},
     publisher = {mathdoc},
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     number = {1},
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     zbl = {0870.39001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1996__32_1_a2/}
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Wong, P. J. Y.; Agarwal, Ravi P. The oscillation of an $m$th order perturbed nonlinear difference equation. Archivum mathematicum, Tome 32 (1996) no. 1, pp. 13-27. http://geodesic.mathdoc.fr/item/ARM_1996__32_1_a2/