IJPAM: Volume 55, No. 4 (2009)

ASYMPTOTIC SOLUTIONS OF
LINEAR DYNAMIC SYSTEMS ON TIME SCALES

Fei Xue
Department of Mathematics
University of Hartford
200, Bloomfield Ave., West Hartford, CT 06117, USA
e-mail: xue@hartford.edu


Abstract.This paper investigates the asymptotic behavior of systems of linear dynamic equations on time scales. By involving a certain integration system we obtain a new set of sufficient conditions under which an asymptotic representation of the perturbed system on time scales can be given. The analogue of Levinson's Perturbation Theorem on time scales is shown to follow from our framework. Further more, some existing theorems for asymptotic behaviors of differential and difference equations are shown to be deduced from the same result.

Received: September 9, 2009

AMS Subject Classification: 39A10, 39A12, 34E10

Key Words and Phrases: time scales, asymptotic behavior, perturbed system, almost diagonal

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 4