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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Attractivity for two-dimensional linear systems whose anti-diagonal coefficients are periodic
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by Jitsuro Sugie and Ayano Endo PDF
Proc. Amer. Math. Soc. 137 (2009), 4117-4127 Request permission

Abstract:

This paper deals with the linear system $\mathbf {x}’ = A(t)\mathbf {x}$ with $A(t)$ being a $2\times 2$ matrix. The anti-diagonal components of $A(t)$ are assumed to be periodic, but the diagonal components are not necessarily periodic. Our concern is to establish sufficient conditions for the zero solution to be attractive. Floquet theory is of no use in solving our problem, because not all components are periodic. Another approach is adopted. Some simple examples are included to illustrate the main result.
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Additional Information
  • Jitsuro Sugie
  • Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan
  • MR Author ID: 168705
  • Email: jsugie@riko.shimane-u.ac.jp
  • Ayano Endo
  • Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan
  • Received by editor(s): March 17, 2009
  • Published electronically: June 19, 2009
  • Additional Notes: The first author was supported in part by a Grant-in-Aid for Scientific Research, No. 19540182, from the Japan Society for the Promotion of Science
  • Communicated by: Yingfei Yi
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 4117-4127
  • MSC (2000): Primary 34D05, 34D20; Secondary 37B25, 37C75
  • DOI: https://doi.org/10.1090/S0002-9939-09-09973-0
  • MathSciNet review: 2538573