Frequent oscillation of a class of partial difference equations (Q1284529)

The authors consider the following partial difference equation \[ A_{m+1,n}+A_{m,n+1}-a_{m,n}A_{m,n}+p_{m,n}A_{m-k,n-\ell}=0 \tag{1} \] where \(k,\ell\) are nonnegative integers, \(\{a_{m,n}\}\) and \(\{p_{m,n}\}\) are real double sequences. Criteria are developed for equation (1) to be frequently oscillatory. Note that if an equation is frequent oscillatory, then it is oscillatory.