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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universal perturbations of linear differential equations


Author: Gerd Herzog
Journal: Proc. Amer. Math. Soc. 130 (2002), 703-705
MSC (1991): Primary 34E10
Published electronically: July 31, 2001
MathSciNet review: 1866023
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Abstract:

Let $X:[0,\infty)\to L(\mathbb{R} ^n)$ be a fundamental solution of $x'=A( t)x$with $X$ and $X^{-1}$ bounded on $[0,\infty)$. We prove that there exist arbitrary small matrix functions $B:[0,\infty)\to L(\mathbb{R} ^n)$ with limit $0$ as $t\to \infty$ such that $y'=(A(t)+B(t))y$ has solutions with $y([0,\infty))$ dense in $\mathbb{R} ^n$.


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Additional Information

Gerd Herzog
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: Gerd.Herzog@math.uni-karlsruhe.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06084-1
PII: S 0002-9939(01)06084-1
Keywords: Linear differential equations, dense orbits, universal elements
Received by editor(s): May 1, 2000
Received by editor(s) in revised form: August 21, 2000
Published electronically: July 31, 2001
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society