Stability Properties and Integrability of the Resolvent of Linear Volterra Equations

Author(s)

Muhammad Islam, University of DaytonFollow
Paul W. Eloe (0000-0002-6590-9931), University of DaytonFollow

Document Type

Article

Publication Date

1995

Publication Source

Tohoku Mathematical Journal

Abstract

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

Inclusive pages

263-269

ISBN/ISSN

0040-8735

Document Version

Published Version

Comments

This document has been made available for download in accordance with the publisher's policy on self-archiving.

Permission documentation on file.

Copyright

Copyright © 1995, Tohoku Mathematical Journal

Publisher

Mathematical Institute of Tohoku University

Volume

47

Issue

2

Place of Publication

Sendai, Japan

Peer Reviewed

yes

eCommons Citation

Islam, Muhammad and Eloe, Paul W., "Stability Properties and Integrability of the Resolvent of Linear Volterra Equations" (1995). Mathematics Faculty Publications. 50.
https://ecommons.udayton.edu/mth_fac_pub/50