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.
Reviewer: Sergei Kornev (Voronezh)
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 |