Displaying similar documents to “Averaging of multivalued differential equations.”

Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Tzanko Donchev (1998)

Colloquium Mathematicae

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Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.

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,...