Karpuz, Başak; Öcalan, Özkan Iterated oscillation criteria for delay partial difference equations. (English) Zbl 1340.39020 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 PDF BibTeX XML Cite \textit{B. Karpuz} and \textit{Ö. Öcalan}, Math. Bohem. 139, No. 3, 437--450 (2014; Zbl 1340.39020) Full Text: Link