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Exponential asymptotic stability for linear volterra equations

Appleby, John A.D. (2000) Exponential asymptotic stability for linear volterra equations. Mathematical Proceedings of the Royal Irish Academy . pp. 1-7. ISSN 1393-7197

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Abstract

This note studies the exponential asymptotic stability of the zero solution of the linear Volterra equation x˙ (t) = Ax(t) + t 0 K(t − s)x(s) ds by extending results in the paper of Murakami “Exponential Asymptotic Stability for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991. In particular, when K isi ntegrable and has entries which do not change sign, and the equation has a uniformly asymptotically stable solution, exponential asymptotic stability can be identified by an exponential decay condition on the entries of K.

Item Type:Article (Published)
Refereed:No
Subjects:Mathematics > Differential equations
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:Royal Irish Academy
Official URL:http://www.ria.ie/publications/journals/ProcAI/100034.html
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:16
Deposited On:26 Oct 2006 by DORAS Administrator. Last Modified 29 Jan 2009 16:38

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