Discrete Dynamics in Nature and Society
Volume 1 (1998), Issue 4, Pages 265-268
doi: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, Qingdao 266003, China
2Department of Mathematics, Binzhou Normal College, Binzhou, Shandong, 256604, China

Received 2 April 1997

Copyright © 1998 B. G. Zhang and S. T. Liu. 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.

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.