On the structure of the set of solutions of a Volterra integral equation in a Banach space
Volume 59 / 1994
Annales Polonici Mathematici 59 (1994), 33-39
DOI: 10.4064/ap-59-1-33-39
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 B₀-space of continuous functions on a noncompact domain.
