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EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES

Part of: Volterra integral equations

Published online by Cambridge University Press:  17 March 2010

MURAT ADıVAR  and
YOUSSEF N. RAFFOUL
MURAT ADıVAR*
Affiliation:
Izmir University of Economics, Department of Mathematics, 35330 Izmir, Turkey (email: murat.adivar@ieu.edu.tr)
YOUSSEF N. RAFFOUL
Affiliation:
University of Dayton, Department of Mathematics, Dayton, OH 45469-2316, USA (email: youssef.raffoul@notes.udayton.edu)
*
✉For correspondence; e-mail: murat.adivar@ieu.edu.tr
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Abstract

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We introduce the concept of ‘shift operators’ in order to establish sufficient conditions for the existence of the resolvent for the Volterra integral equation on time scales. The paper will serve as the foundation for future research on the qualitative analysis of solutions of Volterra integral equations on time scales, using the notion of the resolvent.

Keywords

existenceresolventshift operatortime scalesVolterra integral equation

MSC classification

Secondary: 45D05: Volterra integral equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 139 - 155
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This work was supported by the Scientific and Technological Research Council of Turkey.

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