Extremal selections of multifunctions generating a continuous flow
Copyright policy )Extremal selections of multifunctions generating a continuous flow
Let $F:[0,T]\times\R^n\mapsto 2^{\R^n}$ 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 $y\in \overline{co} F(t,x)$ and $\varepsilon>0$, there exists a Lipschitz selection $��$ of $\overline{co}F$, defined on a neighborhood of $(t,x)$, with $|��(t,x)-y|
18 pages
Cauchy problem, Mathematics - Functional Analysis, unique Carathéodory solution, FOS: Mathematics, differential inclusion, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Ordinary differential inclusions, Functional Analysis (math.FA)
Cauchy problem, Mathematics - Functional Analysis, unique Carathéodory solution, FOS: Mathematics, differential inclusion, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Ordinary differential inclusions, Functional Analysis (math.FA)
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