## Théorème d’existence pour des inclusions différentielles sans convexité. (Existence theorems for differential inclusions without convexity).(French)Zbl 0731.47048

In the paper under review, using the recent selection theorem of Bressan- Colombo [Stud. Math. 90, 70-85 (1988)], the authors establish some general existence results for differential inclusions of the form $y^{(k)}\in F(t,y,...,y^{(k-1)}),$ where y is given homogeneous boundary or initial value data, and the multivalued function $$F: [0,T]\times {\mathbb{R}}^{kn}\to 2^{{\mathbb{R}}^ n}$$ satisfies some hypotheses of measurability and semi-continuity, and has nonempty, compact values which are not necessarily convex.

### MSC:

 47E05 General theory of ordinary differential operators 34G20 Nonlinear differential equations in abstract spaces