## 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

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

global solution

Zbl 0483.47038