Oscillation results on linear systems of difference equations. (English) Zbl 0846.39005
Consider the difference system
\[
a_{n+1}- a_n+ \sum^m_{i=1} Q_i a_{n-k_i} =0, \tag \(*\)
\]
where \(k_i\in \mathbb{Z}\), \(Q_i\in \mathbb{R}^{r\times r}\), \(i=1, 2, \dots, m\). The author establishes explicit conditions for the difference system \((*)\) to be oscillatory. For some special cases of the system \((*)\) these conditions become necessary and sufficient. For related results see the papers of L. Erbe and Q. Kong [Hiroshima Math. J. 24, No. 2, 317-329 (1994; Zbl 0811.34053)] and Q. Kong and H. I. Freedman [Differ. Integral Equ. 6, No. 6, 1325-1336 (1993; Zbl 0780.34049)].
Reviewer: E.Thandapani (Salem)
References:
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