Discrete Dynamics in Nature and Society

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Discrete Dynamics in Nature and Society / 1998 / Article

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Volume 1 |Article ID 240730 | 4 pages | https://doi.org/10.1155/S1026022697000265

Necessary and sufficient conditions for oscillations of linear delay partial difference equations

B. G. Zhang1 and S. T. Liu2

1Department of Applied Mathematics, Ocean University of Qingdao, China

2Department of Mathematics, Binzhou Normal College, Binzhou, Shandong, China

Received02 Apr 1997

Abstract

This paper is concerned with the linear delay partial difference equation Am,n=∑i=1upiAm−ki,n−li+∑j=1vqjAm+τj,n+σj, where pi and qj are r×r matrices, Am,n=(am,n1,am,n2, …,am,nr)T, ki, li , τj and σj are nonnegative integers, u and v are positive integers. Sufficient and necessary conditions for all solutions of this equation to be oscillatory componentwise are obtained.

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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