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Aufsatz / Paper in sonstiger referierter Fachzeitschrift

A constructive comparison technique for determining the asymptotic behaviour of linear functional differential equations with unbounded delay

Buckwar E., Appleby J.: A constructive comparison technique for determining the asymptotic behaviour of linear functional differential equations with unbounded delay, in: Differential Equations and Dynamical Systems, Volume 18, Number 3, Page(s) 271-301, 2010.

BibTeX

@ARTICLE{
title = {A constructive comparison technique for determining the asymptotic behaviour of linear functional differential equations with unbounded delay},
type = {Aufsatz / Paper in sonstiger referierter Fachzeitschrift},
author = {Buckwar, Evelyn and Appleby, John A.D. },
language = {EN},
abstract = {In this paper, we obtain exact non-exponential rates of growth and decay of solutions of linear functional differential equations with unbounded delay. As a by-product, exponential asymptotic stability is ruled out for asymptotically stable solutions of these equations. Equations with maximum functionals on the right hand side, as well as perturbed equations, are considered. We also give examples showing how the rate of growth or decay of solutions depends on the rate of growth of the unbounded delay. The results established here are obtained by constructing carefully functions which satisfy upper and lower differential inequalities and one aim of the paper is to elucidate this constructive comparison technique.},
pages = {271-301},
publisher = {Springer India, New Delhi, India},
journal = {Differential Equations and Dynamical Systems},
volume = {18},
number = {3},
issn = {0971-3514},
year = {2010},
}

Details

Zusammenfassung: In this paper, we obtain exact non-exponential rates of growth and decay of solutions of linear functional differential equations with unbounded delay. As a by-product, exponential asymptotic stability is ruled out for asymptotically stable solutions of these equations. Equations with maximum functionals on the right hand side, as well as perturbed equations, are considered. We also give examples showing how the rate of growth or decay of solutions depends on the rate of growth of the unbounded delay. The results established here are obtained by constructing carefully functions which satisfy upper and lower differential inequalities and one aim of the paper is to elucidate this constructive comparison technique.

Journal: Differential Equations and Dynamical Systems
Volume: 18
Nummer: 3
Erscheinungsjahr: 2010
Seitenreferenz: 271-301
Anzahl Seiten: 31
Verlag: Springer India, New Delhi, India
ISSN: 0971-3514
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Univ.-Prof. Dr. Evelyn Buckwar, John A.D. Appleby

Forschungseinheiten der JKU:

Wissenschaftszweige: 1103 Analysis | 1113 Mathematische Statistik | 1114 Numerische Mathematik | 1118 Wahrscheinlichkeitstheorie | 1121 Operations Research | 1145 Zeitreihenanalyse | 1165 Stochastik | 5943 Risikoforschung

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