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Set differential equations with causal operators. (English) Zbl 1108.34011
Let \(E\) be a Banach space and \(Q\in C(E,E)\) be a causal or nonanticipative operator (see, e.g. [C. Corduneanu, Functional equations with causal operators. London: Taylor & Francis (2002; Zbl 1042.34094)]). The paper is devoted to the study of set differential equations with causal operators of the form \(D_HU(t)=(QU)(t),\) where \(D_H\) is a Hukuhara derivative. Under some assumptions on the operator \(Q\), the authors prove existence, uniqueness and continuous dependence of solutions with respect to initial values.

34A60 Ordinary differential inclusions
34K05 General theory of functional-differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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