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Systems of linear ordinary differential equations with bounded coefficients may have very oscillating solutions
Author(s):
D.
Novikov
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3753-3755.
MSC (1991):
Primary 34C10, 34M10;
Secondary 34C07
Posted:
June 27, 2001
MathSciNet review:
1860513
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Abstract:
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:
-
- 1.
- Yu. Ilyashenko and S. Yakovenko, Counting real zeros of analytic functions satisfying linear ordinary differential equations, Journal of Differential Equations 126 (1996), no. 1, 87-105. MR 97a:34010
- 2.
- D. Novikov and S. Yakovenko, Meandering of trajectories of polynomial vector fields in the affine
 -space, Publ. Mat. 41 (1997), no. 1, 223-242. MR 98f:58160 - 3.
- -, Trajectories of polynomial vector fields and ascending chains of polynomial ideals, Ann. Inst. Fourier 49 (1999), no. 2, 563-609. CMP 99:14
- 4.
- S. Yakovenko, On functions and curves defined by ordinary differential equations, Proceedings of the Arnoldfest (Ed. by E. Bierstone, B. Khesin, A. Khovanskii, J. Marsden), Fields Institute Communications, 1999, pp. 203-219. CMP 2000:08
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Additional Information:
D.
Novikov
Affiliation:
Department of Mathematics, Toronto University, Toronto, Ontario, Canada M5S 3G3
Email:
dmitry@math.toronto.edu
DOI:
10.1090/S0002-9939-01-06120-2
PII:
S 0002-9939(01)06120-2
Keywords:
Bounded oscillation,
linear differential equations
Received by editor(s):
July 31, 2000
Received by editor(s) in revised form:
September 11, 2000
Posted:
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
Copyright of article:
Copyright
2001,
American Mathematical Society
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