Sur l’intervalle maximal d’existence de solutions pour des inclusions différentielles. (On the maximal interval for the existence of solutions to differential inclusions). (French) Zbl 0643.34015

Frigon, Marelène; Granas, Andrzej; Guennoun, Zine-el-abdine

C. R. Acad. Sci., Paris, Sér. I 306, No. 18, 747-750 (1988).

We establish the existence of a global solution for differential inclusions of the form u’(t)\(\in F(t,u(t))\) a.e. in [0,T], \(u(0)=r\), under the suitable conditions on \(F: [0,T]\times {\mathbb{R}}^ n\to 2^{{\mathbb{R}}^ n};\) in the case where F is single-valued and continuous, one recovers a well-known result of Wintner [J. Duguridji and A. Granas, Fixed point theory, Vol. I. (1982; Zbl 0483.47038)].

MSC:

34A60

Ordinary differential inclusions

Keywords:

global solution

Citations:

Zbl 0483.47038