Necessary and sufficient conditions for oscillations of delay partial difference equations (Q1128061)

The authors study two classes of delay partial difference equations of the form \[ \begin{multlined} u(i+1,j)+ bu(i,j+1)+ cu(i,j)+ du(i-r,j)+ eu(i,j-s)+\\ fu(i-m,j-n)=0,\quad i,j=0,1,2,\dots \end{multlined} \] and \[ \begin{multlined} u(i+1,j+1)+ au(i+1,j)+ bu(i,j+1)+ cu(i,j)+ du(i-r,j)+\\ eu(i,j-s)+ fu(i-m,j-n)=0,\quad i,j=0,1,2,\dots, \end{multlined} \] where \(a,b,c,d,e\) and \(f\) are real numbers, \(r,s,m\) and \(n\) are positive integers. Explicit necessary and sufficient conditions for the oscillation of the solutions of these equations are obtained.