Oscillation for partial difference equations with continuous variables.
type: Item
instance of: scholarly article
title: Oscillation for partial difference equations with continuous variables.
zbMATH Open document ID: 1047.39003
DOI: 10.1016/S0377-0427(02)00859-2
author: Baotong Cui
author: Yongqing Liu
published in: Journal of Computational and Applied Mathematics
publication date: 2003-06-17T00:00:00Z
review text: 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.
reviewed by: Sui Sun Cheng
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1929413
zbMATH Keywords: Oscillation
zbMATH Keywords: Partial difference equation
zbMATH Keywords: Continuous variable
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00859-2
OpenAlex ID: W1967967824
description: scientific article; zbMATH DE number 1929413