Proceedings of the American Mathematical Society

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



Systems of linear ordinary differential equations with bounded coefficients may have very oscillating solutions

Author: D. Novikov
Journal: Proc. Amer. Math. Soc. 129 (2001), 3753-3755
MSC (1991): Primary 34C10, 34M10; Secondary 34C07
Published electronically: June 27, 2001
MathSciNet review: 1860513
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Abstract | References | Similar Articles | Additional Information


An elementary example shows that the number of zeroes of a component of a solution of a system of linear ordinary differential equations cannot be estimated through the norm of coefficients of the system.

References [Enhancements On Off] (What's this?)

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  • 2. D. Novikov and S. Yakovenko, Meandering of trajectories of polynomial vector fields in the affine 𝑛-space, Proceedings of the Symposium on Planar Vector Fields (Lleida, 1996), 1997, pp. 223–242. MR 1461653, 10.5565/PUBLMAT_41197_14
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Additional Information

D. Novikov
Affiliation: Department of Mathematics, Toronto University, Toronto, Ontario, Canada M5S 3G3

Keywords: Bounded oscillation, linear differential equations
Received by editor(s): July 31, 2000
Received by editor(s) in revised form: September 11, 2000
Published electronically: June 27, 2001
Additional Notes: The author is grateful to S. Yakovenko for drawing his attention to this problem and for many stimulating discussions, and to C. Chicone for amelioration of the final text. This research was supported by the Killam grant of Prof. Milman.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society