Abstract

In this paper we study the existence and uniqueness of mild solutions to integro-differential equations in terms of a resolvent operator on the interval [0, 2 pi] and on the real line. Moreover, we characterize the spectrum of the resolvent family that solves the Volterra equation u' = Au +(a * Au) + f in terms of their mild periodic solutions. (C) 2019 Elsevier Inc. All rights reserved.