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Existence, uniqueness, and continuous dependence for hereditary differential equations. (English) Zbl 0709.34062
In the setting of functional differential equations, an abstract hereditary structure is introduced which includes and unifies many formulations already considered by other authors, e.g., T. S. Angell [Siam. J. Control Optim. 14, 1-18 (1976; Zbl 0323.49005)], J. K. Hale and M. A. Cruz [Ann. Mat. Pura Appl., IV. Ser. 85, 63- 81 (1970; Zbl 0194.410)], G. S. Jones [Univ. of Maryland Reports (1965) and Math. Syst. Theory 1, 263-278 (1967; Zbl 0154.339)]. In the paper under review, for the new structure, existence, uniqueness, and continuous dependence theorems are given.
Reviewer: H.Haruki

MSC:
34K30 Functional-differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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