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History-dependent decay rates for a logistic equation with infinite delay

Published online by Cambridge University Press:  11 February 2011

John A. D. Appleby ,
István Győri  and
David W. Reynolds
John A. D. Appleby
Affiliation:
Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland (john.appleby@dcu.ie)
István Győri
Affiliation:
Department of Mathematics, University of Pannonia, Pf158, Egyetum u. 10, 8201 Veszprém, Hungary (gyori@almos.uni-pannon.hu)
David W. Reynolds
Affiliation:
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland (david.reynolds@dcu.ie)
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Abstract

A logistic equation with infinite delay is considered under conditions that force its solution to approach a positive steady state at large times. It is shown that this rate of convergence depends on the initial history in some cases, and is independent of the history in others.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 1 , February 2011 , pp. 23 - 44
Copyright
Copyright © Royal Society of Edinburgh 2011

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