Remarks on oscillation and nonoscillation for second-order linear difference equations.

*(English)*Zbl 1161.39014In this remark, the authors consider the second-order linear difference equation

$${{\Delta}}^{2}{x}_{n-1}+{p}_{n}{x}_{n}=0,\phantom{\rule{1.em}{0ex}}n\ge {n}^{0},$$

where ${\left\{{p}_{n}\right\}}_{n=1}^{\infty}$ is a real sequence with ${p}_{n}\ge 0$ for $n\ge {n}^{0}$. The main contribution is two-fold. One is to show that the main results of an earlier work by *W. T. Li* and *S. S. Cheng* [ibid. 16, No. 2, 161–163 (2003; Zbl 1052.39009)] are incorrect. The other is to obtain a generalized criterium about the oscillation and nonoscillation of the equation.

Reviewer: Shangjiang Guo (Hunan)

##### MSC:

39A11 | Stability of difference equations (MSC2000) |

39A10 | Additive difference equations |