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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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