Oscillation for partial difference equations with continuous variables.
Oscillation criteria are established for partial difference equations of the form \[ \begin{multlined} Au(x+a,y+b)+Bu(x+a,y)+Cu(x,y+b)-u(x,y) \\ +D(x,y)u(x-\tau ,y)+E(x,y)u(x,y-\sigma )+F(x,y)u(x-\tau ,y-\sigma )=0, \end{multlined} \] where \(D,E,F:[0,\infty )\times [0,\infty )\rightarrow (0,\infty )\) are continuous, \(A,B,C\) are nonnegative constants, and \(a,b,\tau ,\sigma \) are positive constants. Some of the results extend those of \textit{B. Zhang} [Acta Math. Sinica 42, No. 3, 487--494 (1999; Zbl 1015.39002)], and \textit{R. P. Agarwal} and \textit{Y. Zhou} [Math. Comput. Modelling 31, No. 2--3, 17--29 (2000; Zbl 1042.39511)], and others. The techniques for deriving these criteria are also similar to some of those in the references. It should be noted that the first paper on oscillation of partial difference equations with continuous variables is due to \textit{G. Zhang} [Far East J. Math. Sci. 6, 89--92 (1998; Zbl 1036.39017)] which is not mentioned in this paper for some reason.
scientific article; zbMATH DE number 1929413