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Differential equations over polynomially bounded o-minimal structures

Authors: Jean-Marie Lion, Chris Miller and Patrick Speissegger
Journal: Proc. Amer. Math. Soc. 131 (2003), 175-183
MSC (2000): Primary 26A12, 34E99; Secondary 34E05, 03C64
Published electronically: May 22, 2002
MathSciNet review: 1929037
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Abstract: We investigate the asymptotic behavior at $+\infty$ of non-oscillatory solutions to differential equations $y'=G(t,y), t>a$, where $G\colon\mathbb{R} ^{1+l}\to\mathbb{R} ^l$ is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.

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Additional Information

Jean-Marie Lion
Affiliation: Laboratoire de Topologie, Université de Bourgogne, 21078 Dijon cedex, France
Address at time of publication: IRMAR, Campus Beaulieu, Université Rennes I, 35042 Rennes cedex, France

Chris Miller
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210

Patrick Speissegger
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Address at time of publication: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706

Received by editor(s): April 11, 2000
Received by editor(s) in revised form: August 20, 2001
Published electronically: May 22, 2002
Additional Notes: The second author’s research was supported by NSF Grants DMS-9896225 and DMS-9988855.
The third author’s research was supported in part by NSERC Grant OGP0009070.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2002 American Mathematical Society

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