Integro-differential equations of Volterra type
- 1 August 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 3 (1) , 9-22
- https://doi.org/10.1017/s0004972700045603
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- The Qualitative Behavior of a Nonlinear Volterra EquationProceedings of the American Mathematical Society, 1965