Remarks on oscillation and nonoscillation for second-order linear difference equations (Q926768)

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 \textit{W. T. Li} and \textit{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.