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# Growth Orders Occurring In Expansions Of Hardy-Field Solutions Of Algebraic Differential-Equations

Shackell, John (1995) Growth Orders Occurring In Expansions Of Hardy-Field Solutions Of Algebraic Differential-Equations. Annales de l'institut Fourier, 45 (1). pp. 183-221. ISSN 0373-0956. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:19038)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.

## Abstract

We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no 'sub-term' occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows. Let g be an element of a Hardy field which has an asymptotic series expansion in x, e(x) and lambda, where lambda tends to zero at least as rapidly as some negative power of exp(e(x)). If lambda actually occurs in the expansion, then g cannot satisfy a first-order algebraic differential equation over R(x).

Item Type: Article ASYMPTOTICS; DIFFERENTIAL EQUATIONS; HARDY FIELDS; DIFFERENTIAL ALGEBRA Q Science Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science I.T. Ekpo 25 Oct 2009 09:36 UTC 16 Nov 2021 09:57 UTC https://kar.kent.ac.uk/id/eprint/19038 (The current URI for this page, for reference purposes)
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