On the oscillation of some linear difference equations with periodic coefficients (Q1372087)

The authors establish necessary and sufficient conditions for the oscillation of solutions of the linear difference equation \[ x_{n+1}- x_n+ a_n (px_{n-k}+ qx_{n-l})=0 \] where \(a_n\) is periodic. The results obtained here are discrete analogues of the oscillation results for some linear delay differential equations with periodic coefficients, which were given earlier by the second author [J. Math. Anal. Appl. 162, No. 2, 452-475 (1991; Zbl 0751.34038)].