Uniform asymptotic stability in linear Volterra integrodifferential equations with application to delay systems. (English) Zbl 0970.45004

In this interesting paper the authors give necessary and sufficient conditions for uniform asymptotic stability in a system of linear Volterra integrodifferential equations. Three examples are also given to explain the view points. A similar result and an example are also presented for functional differential equations under suitable assumptions.
The application of the results to delay systems is pointed out. The theorems established herein are direct extensions of R. K. Miller’s well known results on uniform stability and uniform asymptotic stability [J. Differ. Equations 10, 485-506 (1971; Zbl 0206.41604)].
Reviewer: K.C.Gupta (Jaipur)


45J05 Integro-ordinary differential equations
45M05 Asymptotics of solutions to integral equations
45M10 Stability theory for integral equations
45F05 Systems of nonsingular linear integral equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations


Zbl 0206.41604