Oscillation theorems for certain nonlinear delay partial difference equations (Q1567531)

The author is concerned with possible relations between the linear partial difference equation \[ A_{m-1, n}+ A_{m,n- 1}- pA_{mn}+ qA_{m+k, n+l}= 0,\quad m,n= 0,1,2,\dots,\tag{1} \] and the nonlinear equation \[ A_{m-1, n}+ A_{m,n-1}- pA_{mn}+ q_{mn}f (A_{m+ k,n+l})= 0,\quad m,n= 0,1,2,\dots,\tag{2} \] where \(k\), \(l\) are positive integers, \(p,q>0\) and \(f\) is a continuous function. Under appropriate conditions, the author claims that every subexponential solution to (1) is oscillatory (i.e., neither eventually positive nor eventually negative for all large \(m\), \(n\)) if, and only if, every subexponential solution to (2) is oscillatory.