Oscillation of second-order linear difference equations (Q5918040)

The author obtains new oscillation and nonoscillation criteria for the self-adjoint difference equation \[ \Delta(c_{n-1}\Delta x_{n-1})+ a_nx_n=0 \] in terms of the sequence \(\sqrt{q_n}= c_n/ \sqrt{b_nb_{n-1}}\) where \(b_n=c_n+ c_{n-1}-a_n\). Further, a necessary and sufficient condition for oscillation is given in the case of \(q_n\) is periodic with period 2. For related results see the papers of \textit{J. W. Hooker}, \textit{M. K. Kwong} and \textit{W. T. Patula} [SIAM J. Math. Anal. 18, 54-63 (1987; Zbl 0619.39005) and J. Math. Anal. Appl. 107, 182-196 (1985; Zbl 0576.39002)].