Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation-Reference-Cited by-同舟云学术

Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation

Published:2013-11-01 Issue:3 Volume:21 Page:17-32
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
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Author:

Advar Murat¹,Raffoul Youssef N.²

Affiliation:

1. 1Department of Mathematics, Izmir University of Economics, Sakarya Cad. No: 156, 35330 Balova, zmir, Turkey

2. 2Department of Mathematics, University of Dayton, Dayton, OH 45469-2316 USA

Abstract

AbstractWe consider the system of Volterra integro-dynamic equations

and obtain necessary and sufficient conditions for the uniform stability of the zero solution employing the resolvent equation coupled with the variation of parameters formula. The resolvent equation that we use for the study of stability will have to be developed since it is unknown for time scales. At the end of the paper, we furnish an example in which we deploy an appropriate Lyapunov functional. In addition to generalization, the results of this paper provides improvements for its counterparts in integro-differential and integro-difference equations which are the most important particular cases of our equation.

Publisher

Walter de Gruyter GmbH

Link

https://content.sciendo.com/downloadpdf/journals/auom/21/3/article-p17.xml

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