Necessary and sufficient conditions for oscillations of delay partial difference equations
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.
scientific article; zbMATH DE number 1186816