Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(4): 933-942

Printed July 31, 2014

https://doi.org/10.4134/BKMS.2014.51.4.933

Copyright © The Korean Mathematical Society.

Representations of solutions to periodic continuous linear system and discrete linear system

Dohan Kim and Jong Son Shin

Seoul National University, Hosei University

Abstract

We give a representation of the component of solutions with characteristic multiplier $1$ in a periodic linear inhomogeneous continuous system. It follows from this representation that asymptotic behaviors of the component of solutions to the system and to its associated homogeneous system are quite different, though they are similar in the case where the characteristic multiplier is not $1$. Moreover, the representation is applicable to linear discrete systems with constant coefficients.

Keywords: representation of solutions, periodic linear continuous system, linear discrete system

MSC numbers: Primary 34A30, 39A06

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