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

Abstract

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