Shen, Jianhua; Stavroulakis, I. P. Oscillation criteria for delay difference equations. (English) Zbl 0964.39009 Electron. J. Differ. Equ. 2001, Paper No. 10, 15 p. (2001). The authors obtain sufficient conditions to assure that all the solutions of the delay difference equation \(x_{n+1}-x_n+p_n x_{n-k}=0\), \(n=0,1, 2, \ldots\) are oscillatory. Here \(\{p_n\}\) is a sequence of nonnegative real numbers and \(k\) is a positive integer. In the considered cases they do not assume one of the well known oscillation conditions \[ \limsup_{n\to\infty}{\sum_{i=0}^{k}{p_{n-i} }} >1 \quad \text{ and } \quad \liminf_{n\to\infty}{\frac{1}{k}\sum_{i=1}^{k}{p_{n-i}}} > \frac{k^k}{(k+1)^{k+1}}. \]Previously, the authors proved some results in which necessary conditions to have a non oscillatory solution were given. Reviewer: Alberto Cabada (Santiago de Compostela) Cited in 16 Documents MSC: 39A11 Stability of difference equations (MSC2000) Keywords:oscillation; non-oscillation; delay difference equation PDFBibTeX XMLCite \textit{J. Shen} and \textit{I. P. Stavroulakis}, Electron. J. Differ. Equ. 2001, Paper No. 10, 15 p. (2001; Zbl 0964.39009) Full Text: EuDML EMIS