Existence, uniqueness, and continuous dependence for hereditary differential equations.

*(English)*Zbl 0709.34062In 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 |

##### Keywords:

functional differential equations; hereditary structure; existence; uniqueness; continuous dependence
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\textit{P. Brandi} and \textit{R. Ceppitelli}, J. Differ. Equations 81, No. 2, 317--339 (1989; Zbl 0709.34062)

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##### References:

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