Existence,uniqueness and continuous dependence for hereditary systems

Summary An hereditary system is a system whose present state is determined in some way by its past history. We formulate a class of such systems which includes functional differential equations of retarded type and many equations of neulral type as well as Volterra integral equations. Theorems of existence, uniqueness, continuation and continuous dependence are proved. Preparation of this paper was sponsored in part by the Office of Naval Research under Contract NONR 233(76). Reproduction in whole or in part is permitted for any purpose of the United States Government. Entrata in Redazione il 22 gennaio 1969.