Deux propriétés des trajectoires d’une équation différentielle multivoque. (French) Zbl 0356.49024

Trav. Semin. d’Anal. convexe, Vol. 5, Expose No. 12, 13 p. (1975).
This paper is essentially an exposition of some results of N. Kikuchi on the properties of trajectories of contingent equations, published in papers which are little known and difficult to read [Publ. Res. Inst. Math. Sci., Kyoto Univ., Ser. A 3, 177–201 (1967; Zbl 0189.47301); ibid. 3, 361–371 (1968; Zbl 0197.13106)]. The properties in questions are the connectedness of the attainability set, under the assumption that the right-hand side of the contingent equation satisfies the conditions of Carathéodory. The proofs given here are modifications of those of Kikuchi.
Reviewer: P. Kloeden


93B05 Controllability
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations