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

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.