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Oscillation of first order neutral delay difference equations. (English) Zbl 1027.39003
Consider the neutral delay difference equation of the form \[ \Delta(y_n+ h_n y_{n-k})+\delta q_n f(y_{n-1}),\quad n= 0,1,\dots,\tag{\(*\)} \] where \(\delta= \pm 1\), \((h_n)\) and \((q_n)\) are positive real sequences and \(f: \mathbb{R}\to\mathbb{R}\) is a continuous function such that \(uf(u)> 0\) for \(u\neq 0\). Under some additional suppositions all solutions to \((*)\) are oscillatory.

MSC:
39A11 Stability of difference equations (MSC2000)
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