On continuous and measurable selections and the existence of solutions of generalized differential equations

Henry Hermes
1971 Proceedings of the American Mathematical Society  
Let C(B") denote the space of nonempty compact subsets of some bounded set Bn in Euclidean n dimensional space En, topologized with the Hausdorff metric topology. The existence of a solution to the initial value problem for the generalized differential equation is shown under the assumption that R:En-»6(5") has bounded variation in some neighborhood of the initial value, and under a less restrictive condition on the variation of R. Included are continuous and Lipschitz continuous selection
more » ... uous selection results for mappings Q'.E1-»C(S") which are, respectively, of bounded variation and Lipschitz continuous. Received by the editors July 31, 1970. A MS 1970 subject classifications. Primary 34A99.
doi:10.1090/s0002-9939-1971-0277794-3 fatcat:redmivai4rggvc5nd3o4aqcfou