Continuous branches of multivalued mappings with nonconvex right side

This paper considers multivalued mappings which map a compact metric space into the space of nonempty closed subsets of $L_I^1$. A theorem asserting the existence of a continuous branch of such a mapping is proved. This theorem is analogous to a theorem of Michael. As corollaries, theorems on the existence of fixed points of multivalued mappings and on the existence of solutions of differential inclusions are proved.
Bibliography: 13 titles.