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

Karpuz, Başak; Öcalan, Özkan

Math. Bohem. 139, No. 3, 437-450 (2014).

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

Keywords:

oscillation criterion; linear partial difference equation

Citations:

Zbl 0877.39012