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Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

Editor-in-Chief: Flaut, Cristina

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

Murat Advar
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  • Department of Mathematics, Izmir University of Economics, Sakarya Cad. No: 156, 35330 Balova, zmir, Turkey
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/ Youssef N. Raffoul
Published Online: 2014-03-05 | DOI: https://doi.org/10.2478/auom-2013-0039


We 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.

Keywords: Lyapunov functional; New resolvent equation; Time scales; Uniform stability; Volterra


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About the article

Published Online: 2014-03-05

Published in Print: 2013-11-01

Citation Information: Analele Universitatii "Ovidius" Constanta - Seria Matematica, Volume 21, Issue 3, Pages 17–32, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/auom-2013-0039.

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