Summary: We shall be concerned with the existence of global solutions to the initial value problem for systems of differential inclusions of the type
is a multifunction with nonempty compact values satisfying some conditions of measurability, and upper or lower semi-continuity;
, the above Cauchy problem was treated in our notes [C. R. Acad. Sci., Paris, Sér. I 306, No. 18, 747-750 (1988; Zbl 0643.34015
); ibid. 310, No. 12, 819-822 (1990; Zbl 0731.47048
)]. However, for
, the established results are new even in the case where
is a single valued Carathéodory or a continuous function.