On the uniform asymptotic stability for a linear integro-differential equation of Volterra type

In this paper, we give a necessary and sufficient condition on the uniform asymptotic stability of the zero solution of a linear integro-differential equation of Volterra type where the ordinary part is ax(t). We put emphasis on the case a>0. The proofs of our results are carried out by using the root analysis of the characteristic equation. In Section 5 we give some conjectures.