An oscillation theorem for a second order nonlinear difference equation. (English) Zbl 0793.39002

Li, Horng Jaan; Cheng, Sui Sun

Util. Math. 43, 155-159 (1993).

A necessary condition for the fact that every solution of the difference equation \(\Delta (p_{n-1}^{-1} \Delta x_{n-1})+q_ n f(x_ n)=0\), \(n=1,2,3,\dots\), over \(\mathbb{R}\) is oscillatory, is given. Here \(p_ n>0\) 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.

Reviewer: H.Länger (Wien)

MSC:

39A10

Additive difference equations

Keywords:

second order nonlinear difference equation; oscillatory solution