Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-16
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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)∥2→0 as t→0 and the length of the solution curve of x is finite (resp., infinite) for every x≠0.
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.
American Psychological Association (APA)
Naito, Yūki& Pašić, Mervan. 2013. Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-494988
Modern Language Association (MLA)
Naito, Yūki& Pašić, Mervan. Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations. International Journal of Differential Equations No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-494988
American Medical Association (AMA)
Naito, Yūki& Pašić, Mervan. Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-494988
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494988