Title

On Asymptotic Equivalence Of Perturbed Linear Systems Of Differential And Difference Equations

Document Type

Article

Publication Date

1-1-2007

Publication Title

Journal Of Mathematical Analysis And Applications

Department

Mathematics and Computer Science

Abstract

Standard results on asymptotic integration of systems of linear differential equations give sufficient conditions which imply that a system is strongly asymptotically equivalent to its principal diagonal part. These involve certain dichotomy conditions on the diagonal part as well as growth conditions on the off-diagonal perturbation terms. Here, we study perturbations with a triangularly-induced structure and see that growth conditions can be substantially weakened. In addition, we give results for not necessarily triangular perturbations which in some sense “interpolate” between the classical theorems of Levinson and Hartman–Wintner. Some analogous results for systems of linear difference equations are also given.

Volume

326

Issue

2

pp.

1174-1189

ISSN

0022-247X