Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations | Zendy

Yūki Naito | Zendy; Mervan Pašić | Zendy

Open Access

Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations

Author(s) -

Yūki Naito,

Mervan Pašić

Publication year - 2013

Publication title -

international journal of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 20

eISSN - 1687-9651

pISSN - 1687-9643

DOI - 10.1155/2013/740980

Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , singularity , zero (linguistics) , polynomial , matrix (chemical analysis) , differential equation , linear differential equation , function (biology) , linguistics , philosophy , physics , materials science , quantum mechanics , evolutionary biology , composite material , biology

We study a new kind of asymptotic behaviour near for the nonautonomous system of two linear differential equations: , , where the matrix-valued function has a kind of singularity at . It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that as and the length of the solution curve of is finite (resp., infinite) for every . It is characterized in terms of certain asymptotic behaviour of the eigenvalues of near . Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at

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