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On regularization of right hand sides of differential relations

Published online by Cambridge University Press:  14 November 2011

Jaroslav Kurzweil  and
Jiří Jarník
Jaroslav Kurzweil
Affiliation:
Ceskoslovenska Akademie Ved, Matematicky Ustav, 11567 Praha 1, Czechoslovakia
Jiří Jarník
Affiliation:
Ceskoslovenska Akademie Ved, Matematicky Ustav, 11567 Praha 1, Czechoslovakia
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Synopsis

Let the values of F be convex compact subsets of Rn and let F be upper semicontinuous with respect to x. There are two ways known of replacing F by a more regular map so that the set of solutions of (2) remains unchanged. We prove that both ways lead to the same more regular map and extend the results to the case where Rn is replaced by a separable Banach space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 151 - 159
Copyright
Copyright © Royal Society of Edinburgh 1984

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