Necessary and sufficient conditions for oscillations of partial difference equations with continuous variables (Q1963119)

The authors obtain sufficient and necessary conditions for all solutions to the partial difference equation \[ A(x+1,y)+ A(x,y+1)-A(x,y)+ pA(x-\sigma,y -\delta)=0 \] to be oscillatory. These results generalize those of \textit{B. G. Zhang} and \textit{S. T. Liu} [Nonlinear Studies 3, No. 2, 187-192 (1996; Zbl 0864.39006)] and of \textit{G. Ladas}, \textit{L. Pakula} and \textit{Z. Wang} [Panam. Math. J. 2, No. 1, 17-26 (1992; Zbl 0773.39002)].