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Integro-differential equations of Volterra type

Published online by Cambridge University Press:  17 April 2009

M. Rama Mohana Rao  and
Chris P. Tsokos
M. Rama Mohana Rao
Affiliation:
Indian Institute of Technology Kanpur, Kanpur, India;
Chris P. Tsokos
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA.
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Abstract

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The aim of this paper is concerned with studying the stability properties of an integro-differential system by reducing it into a scalar integro-differential equation. A theorem is stated about the existence of a maximal solution of such systems and a basic result on integro-differential inequalities. Utilizing these results we obtain sufficient conditions for uniform asymptotic stability of the trivial solution of the integro-differential system of the form where , with , , C(J) denotes the space of continuous functions, A a continuous operator such that A maps C(J) into C(J). The fruitfulness of the results of the paper are illustrated with two applications.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 9 - 22
Copyright
Copyright © Australian Mathematical Society 1970

References

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