Differential equations over polynomially bounded o-minimal structures

Lion, Jean-Marie; Miller, Chris; Speissegger, Patrick

doi:10.1090/S0002-9939-02-06509-7

Differential equations over polynomially bounded o-minimal structures
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by Jean-Marie Lion, Chris Miller and Patrick Speissegger PDF

Proc. Amer. Math. Soc. 131 (2003), 175-183 Request permission

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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