Oscillations of the system of linear nonautonomous difference equations. (Q1404909)

The authors consider the system of linear nonautonomous difference equations \(x_{n+1}-x_n+P(n)x_{n-k}\), \(n=0, 1, 2, \dots\), where \(k\in \mathbb{Z}\), \(P(n)\in \mathbb{R}^{r\times r}\) and obtain sufficient conditions for the system to be oscillatory. But the proof of the main theorem (Theorem 2.1) is incorrect, since Lemma 1.1 for an autonomous system is applied to the nonautonomous system in the proof of Theorem 2.1. Theorem 2.3 and Theorem 2.4 are obviously incorrect.