On the structure of the set of solutions of a Volterra integral equation in a Banach space

Abstract

Abstract. The set of solutions of a Volterra equation in a Banach space with a Carathéodory kernel is proved to be an R δ , in particular compact and connected. The kernel is not assumed to be uniformly continuous with respect to the unknown function and the characterization is given in terms of a B 0 -space of continuous functions on a noncompact domain.