STABILITY PROPERTIES AND INTEGRABILITY OF THE RESOLVENT OF LINEAR VOLTERRA-EQUATIONS

Integrability of the resolvent and the stability properties of the zer o solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stabl e if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if a nd only if the resolvent iss integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the inte grability of the resolvent is obtained under an explicit condition.