Existence, Uniqueness and Continuous Dependence for Hereditary Systems

摘要

An hereditary system is a system whose present state is determined in some way by its past history. In this paper, a class of hereditary systems is formulated which includes all functional differential equations of retarded type, Volterra integral equations and difference equations. The formulation does not include all functional differential equations of neutral type the basic restriction being that the derivative x dot occurs linearly in the equations. The report contains theorems of existence, uniqueness and continuation of solutions, as well as theorems on the dependence of solutions on initial data and parameters. (Author)