Existence, Uniqueness, and continuous Dependence for Hereditary Differential Equations

In the setting of functional differential equations, an abstract hereditary structure is introduced which includes and unifies many formulations already considered by other authors. For the new structure, existence, uniqueness, and continuous dependence theorems are given. The setting includes several classes of functional-differential equations. The lag function need not be continuous nor be a compact connected-valued map. This formulation permits us to consider systems in which the presence of holes in the past does not influence the present state of the system, systems which tend to forget the more distant past, systems with sudden memory voids.