On continuous and measurable selections and the existence of solutions of generalized differential equations
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- by Henry Hermes PDF
- Proc. Amer. Math. Soc. 29 (1971), 535-542 Request permission
Abstract:
Let $\mathcal {C}({B^n})$ denote the space of nonempty compact subsets of some bounded set ${B^n}$ in Euclidean n dimensional space ${E^n}$, topologized with the Hausdorff metric topology. The existence of a solution to the initial value problem for the generalized differential equation $dx(t)/dt \in R(x(t))$ is shown under the assumption that $R:{E^n} \to \mathcal {C}({B^n})$ 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 results for mappings $Q:{E^1} \to \mathcal {C}({B^n})$ which are, respectively, of bounded variation and Lipschitz continuous.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 535-542
- MSC: Primary 34.04
- DOI: https://doi.org/10.1090/S0002-9939-1971-0277794-3
- MathSciNet review: 0277794