<abstract xmlns="http://www.w3.org/1999/xhtml"><sec><p>We consider the system of Volterra integro-dynamic equations
				 </p><disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/17.png"></inline-graphic></disp-formula><p>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.</p></sec></abstract>

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.

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

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

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

We consider the system of Volterra integro-dynamic equations
				 and obtain necessary and sufficient conditions for the uniform stability of the zero solution...

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

Published Online: Mar 05, 2014

Page range: 17 - 32

DOI: https://doi.org/10.2478/auom-2013-0039

Keywords
Lyapunov functional, New resolvent equation, Time scales, Uniform stability, Volterra

This content is open access.

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

Published Online: Mar 05, 2014

Page range: 17 - 32

DOI: https://doi.org/10.2478/auom-2013-0039

KeywordsLyapunov functional, New resolvent equation, Time scales, Uniform stability, Volterra

This content is open access.

Keywords
Lyapunov functional, New resolvent equation, Time scales, Uniform stability, Volterra