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 available from this repository)

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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
Uncontrolled keywords: ASYMPTOTICS; DIFFERENTIAL EQUATIONS; HARDY FIELDS; DIFFERENTIAL ALGEBRA
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: I.T. Ekpo
Date Deposited: 25 Oct 2009 09:36
Last Modified: 16 Apr 2014 10:16
Resource URI: http://kar.kent.ac.uk/id/eprint/19038 (The current URI for this page, for reference purposes)
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