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Iterated oscillation criteria for delay partial difference equations. (English) Zbl 1340.39020

The authors consider the linear partial difference equation \(x(m+1,n)+x(m,n+1)-x(m,n)+p(m,n)x(m-k,n-l)=0\) on \(\mathbb{N}_0\times\mathbb{N}_0\), where \(p\) is a nonnegative double sequence of reals and \(k,l\in\mathbb{N}_0\). A modified definition of oscillation of a double sequence is introduced. The main result of the paper is a sufficient condition guaranteeing oscillation of all solutions of the equation. These results can be seen as an improvement of the criterion proved by B. G. Zhang and S. T. Liu [J. Math. Anal. Appl. 206, No. 2, 480–492 (1997; Zbl 0877.39012)].
Reviewer: Pavel Rehak (Brno)

MSC:

39A21 Oscillation theory for difference equations
39A14 Partial difference equations
39A12 Discrete version of topics in analysis
35R10 Partial functional-differential equations

Citations:

Zbl 0877.39012
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