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2013 Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations
Yūki Naito, Mervan Pašić
Int. J. Differ. Equ. 2013(SI2): 1-11 (2013). DOI: 10.1155/2013/740980

Abstract

We study a new kind of asymptotic behaviour near t=0 for the nonautonomous system of two linear differential equations: x'(t)=A(t)x(t), t(0,t0], where the matrix-valued function A=A(t) has a kind of singularity at t=0. It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that x(t)20 as t0 and the length of the solution curve of x is finite (resp., infinite) for every x0. It is characterized in terms of certain asymptotic behaviour of the eigenvalues of A(t) near t=0. Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at t=0.

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Yūki Naito. Mervan Pašić. "Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations." Int. J. Differ. Equ. 2013 (SI2) 1 - 11, 2013. https://doi.org/10.1155/2013/740980

Information

Received: 2 April 2013; Accepted: 21 May 2013; Published: 2013
First available in Project Euclid: 24 January 2017

zbMATH: 1294.34011
MathSciNet: MR3073180
Digital Object Identifier: 10.1155/2013/740980

Rights: Copyright © 2013 Hindawi

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