For linear Volterra integrodifferential equations, we characterize the uniform asymptotic stability property of the zero solution by a property for the resolvent operator. In particular, for equations of convolution type, we characterize the uniform asymptotic stability property in terms of the integrability of the resolvent operator, as well as the invertibility of the characteristic operator. Furthermore, we apply our results to nonhomogeneous equations with asymptotically almost periodic forcing terms, and establish some results on the existence of asymptotically almost periodic solutions.
Funkcialaj Ekvacioj 48 (3), 367-392, 2005
Division of Functional Equations, The Mathematical Society of Japan