Hereditary differential systems with constant delays. I. General case

This paper presents a discussion of the structure of hereditary differential systems defined on a Banach space with initial data in the space of p-integrable maps. Both finite and infinite time histories are allowed. A unified approach to Global and Local Cauchy problems on finite or infinite time intervals is presented. An existence theorem for Carathéodory systems and an existence and uniqueness theorem for Lipschitz systems are derived. In both cases continuity of a solution with respect to the initial data is established.