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ISSN 1088-6826(e) ISSN 0002-9939(p)

Attractivity for two-dimensional linear systems whose anti-diagonal coefficients are periodic

Author(s): Jitsuro Sugie; Ayano Endo
Journal: Proc. Amer. Math. Soc. 137 (2009), 4117-4127.
MSC (2000): Primary 34D05, 34D20; Secondary 37B25, 37C75
Posted: June 19, 2009
MathSciNet review: 2538573
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Abstract: This paper deals with the linear system $\mathbf{x}' = A(t)\mathbf{x}$ with being a $2\times2$ matrix. The anti-diagonal components of 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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