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- W4298012008 abstract "Let $F:[0,T]timesR^nmapsto 2^{R^n}$ be a continuous multifunction with compact, not necessarily convex values. In this paper, we prove that, if $F$ satisfies the following Lipschitz Selection Property: begin{itemize} item[{(LSP)}] {sl For every $t,x$, every $yin overline{co} F(t,x)$ and $varepsilon>0$, there exists a Lipschitz selection $phi$ of $overline{co}F$, defined on a neighborhood of $(t,x)$, with $|phi(t,x)-y|<varepsilon$.} end{itemize} then there exists a measurable selection $f$ of $ext F$ such that, for every $x_0$, the Cauchy problem $$ dot x(t)=f(t,x(t)),qquadqquad x(0)=x_0 $$ has a unique Caratheodory solution, depending continuously on $x_0$. We remark that every Lipschitz multifunction with compact values satisfies (LSP). Another interesting class, for which (LSP) holds, consists of those continuous multifunctions $F$ whose values are compact and have convex closure with nonempty interior." @default.
- W4298012008 created "2022-10-01" @default.
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- W4298012008 date "1992-09-09" @default.
- W4298012008 modified "2023-10-17" @default.
- W4298012008 title "Extremal Selections of Multifunctions Generating a Continuous Flow" @default.
- W4298012008 doi "https://doi.org/10.48550/arxiv.funct-an/9209001" @default.
- W4298012008 hasPublicationYear "1992" @default.
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