Asymptotic behavior and oscillation of delay partial difference equations with positive and negative coefficients (Q1430429)

The authors find some sufficient conditions in order that all the solutions of the linear partial difference equations \[ A_{m-1,n}+A_{m,n-1}-A_{mn}+pA_{m+k,n+l}-qA_{m+k^{\prime },n+l^{\prime }}=0 \] and \[ A_{m-1,n}+A_{m,n-1}-A_{mn}+p_{mn}A_{m+k,n+l}-q_{mn}A_{m+k^{\prime },n+l^{\prime }}=0 \] to oscillate. Here \(m,n,k,k^{\prime },l,l^{\prime }\) are nonnegative integers, \(p,q\in \left( 0,\infty \right) \) and \(\left\{ p_{mn}\right\} ,\) \(\left\{ q_{mn}\right\} \) are sequences of nonnegative real numbers. The above delay equations have positive and negative coefficients.