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Zbl 1161.39014
Zhou, Yong; Zhang, B.G.; Li, C.F.
Remarks on oscillation and nonoscillation for second-order linear difference equations. (English)
[J] Appl. Math. Lett. 21, No. 6, 578-580 (2008). ISSN 0893-9659

In this remark, the authors consider the second-order linear difference equation $$ \Delta^2x_{n-1}+p_nx_n=0,\quad n\geq n^0, $$ where $\{p_n\}^{\infty}_{n=1}$ is a real sequence with $p_n\geq 0$ for $ n\geq n^0$. The main contribution is two-fold. One is to show that the main results of an earlier work by {\it W. T. Li} and {\it 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.
[Shangjiang Guo (Hunan)]

MSC 2000:: *39A11 Stability of difference equations
39A10 Difference equations

Keywords: oscillation; nonoscillation; second-order linear difference equation

Citations: Zbl 1052.39009

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Zentralblatt MATH Berlin [Germany]