Linear Asymptotic Equilibrium of Nilpotent Systems of Linear Difference Equations

William F. Trench
1999 Journal of difference equations and applications (Print)  
We give sufficient conditions for a k×k linear system of difference equations ∆xn = Anxn, n = 0, 1, . . . , to have linear asymptotic equilibrium if An = a1(n)Q+· · ·+ap(n)Q p , where Q p+1 = 0 for some p ∈ {1, 2, . . . , k−1} and {a1(n)} ∞ n=0 , . . . , {ap(n)} ∞ n=0 are sequences of scalars. The conditions involve convergence (perhaps conditional) of certain iterated sums involving these sequences.
doi:10.1080/10236199908808207 fatcat:cvsxjiqdmzehlmzqhybt3jlw54