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.
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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: | https://kar.kent.ac.uk/id/eprint/19038 (The current URI for this page, for reference purposes) |

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