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Zbl 0793.39002
Li, Horng Jaan; Cheng, Sui Sun
An oscillation theorem for a second order nonlinear difference equation. (English)
[J] Util. Math. 43, 155-159 (1993). ISSN 0315-3681

A necessary condition for the fact that every solution of the difference equation $\Delta (p\sb{n-1}\sp{-1} \Delta x\sb{n-1})+q\sb n f(x\sb n)=0$, $n=1,2,3,\dots$, over $\bbfR$ is oscillatory, is given. Here $p\sb n>0$ for all $n$, $f$ is nondecreasing with $\text {sign} f(x)=\text {sign} x$ and a sequence of real numbers is called oscillatory if it is neither eventually positive nor eventually negative.
[H.Länger (Wien)]

MSC 2000:: *39A10 Difference equations

Keywords: second order nonlinear difference equation; oscillatory solution

Cited in: Zbl 1025.39010

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