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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.

MSC:
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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