On the oscillation of certain difference equations. (English) Zbl 0969.39005

Grace, S. R.; El-Morshedy, H. A.

Math. Bohem. 125, No. 4, 421-430 (2000).

Summary: We study the oscillation of difference equations of the form \[ \Delta ^{2}x_{n}+p_{n}\Delta x_{n}+f(n, x_{n-g}, \Delta x_{n-h})=0, \] in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation \[ \Delta ^{2}x_{n}+p_{n}\Delta x_{n}+q_{n}|x_{n-g}|^{\lambda}|\Delta x_{n-h}|^{\mu}\text{ sgn } x_{n-g}=0, \] where \(\lambda \) and \(\mu \) are real constants, \(\lambda >0\) and \(\mu \geq 0\).

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

oscillation; delay difference equations; forced equations