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Displaying similar documents to “Generalized flow invariance for differential inclusions.”

Extremal selections of multifunctions generating a continuous flow

Alberto Bressan, Graziano Crasta (1994)

Annales Polonici Mathematici

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Let F : [ 0 , T ] × ℝ n → 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: (LSP) For every t,x, every y ∈ c̅o̅F(t,x) and ε > 0, there exists a Lipschitz selection ϕ of c̅o̅F, defined on a neighborhood of (t,x), with |ϕ(t,x)-y| < ε, then there exists a measurable selection f of ext F such that, for every x₀, the Cauchy problem ẋ(t) = f(t,x(t)), x(0) = x₀, has a unique Carathéodory solution,...