Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic stability for three-dimensional linear differential systems with time-varying coefficients

Authors: Jitsuro Sugie and Yuichi Ogami
Journal: Quart. Appl. Math. 67 (2009), 687-705
MSC (2000): Primary 34D05, 34D20, 34D23; Secondary 37B25, 37B55
DOI: https://doi.org/10.1090/S0033-569X-09-01133-X
Published electronically: May 27, 2009
MathSciNet review: 2588230
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the asymptotic stability of the zero solution of three-dimensional linear differential systems with variable coefficients. The coefficients are not assumed to be positive. A concept innovated by László Hatvani plays a vital role in our results. Sufficient conditions are also given for the zero solution to be uniformly stable. Some suitable examples are included to illustrate our results. Finally, certain changes of variable are used to broaden the application of our results.

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Additional Information

Jitsuro Sugie
Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan
Email: jsugie@riko.shimane-u.ac.jp

Yuichi Ogami
Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan

DOI: https://doi.org/10.1090/S0033-569X-09-01133-X
Keywords: Uniform stability, asymptotic stability, linear differential systems, weakly integrally positive.
Received by editor(s): May 8, 2008
Published electronically: May 27, 2009
Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research, No. 19540182
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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