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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 selectiondoi:10.1090/s0002-9939-1971-0277794-3 fatcat:redmivai4rggvc5nd3o4aqcfou