Alberto Bressan,
Graziano Crasta
(1994)
Let 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,...