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March 2008 Floquet representations and asymptotic behavior of solutions to periodic linear difference equations
T. Naito, P. H. A. Ngoc, J. S. Shin
Hiroshima Math. J. 38(1): 135-154 (March 2008). DOI: 10.32917/hmj/1207580348

Abstract

We give new representations of solutions for the periodic linear difference equation of the type $x(n+1)=B(n)x(n)+b(n)$, where complex nonsingular matrices $B(n)$ and vectors $b(n)$ are $\rho$-periodic. These are based on the Floquet multipliers and the Floquet exponents, respectively. By using these representations, asymptotic behavior of solutions is characterized by initial values. In particular, we can characterize necessary and sufficient conditions that the equation has a bounded solution(or a $\rho$-periodic solution), and the Massera type theorem by initial values.

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T. Naito. P. H. A. Ngoc. J. S. Shin. "Floquet representations and asymptotic behavior of solutions to periodic linear difference equations." Hiroshima Math. J. 38 (1) 135 - 154, March 2008. https://doi.org/10.32917/hmj/1207580348

Information

Published: March 2008
First available in Project Euclid: 7 April 2008

zbMATH: 1148.39008
MathSciNet: MR2397383
Digital Object Identifier: 10.32917/hmj/1207580348

Subjects:
Primary: 39A10, 39A11

Rights: Copyright © 2008 Hiroshima University, Mathematics Program

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Vol.38 • No. 1 • March 2008
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