Oscillation of neutral delay difference equations (Q675972)

The authors obtain sufficient conditions for the oscillation of all solutions of \[ \Delta (x_n-x_{n-k}) +p_nx_{n-1} =0,\;n=0,1,2, \dots. \] By using the result obtained, a necessary and sufficient condition for all solutions of \[ \Delta (x_n-x_{n-k}) +n^{-\alpha} x_{n-1} =0,\;n=0,1,2, \dots \] to oscillate, where \(\alpha\) is a real number, is established. For related results see the papers of \textit{M. P. Chen}, \textit{B. S. Lalli} and \textit{J. S. Yu} [Comput. Math. Applic. 29, No. 3, 5-11 (1995; Zbl 0819.39004)] and \textit{J. S. Yu}, \textit{B. G. Zhang} and \textit{Z. C. Wang} [Appl. Anal. 53, No. 1-2, 117-124 (1994; Zbl 0839.39001)].