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On the density of extremal solutions of differential inclusions

F. S. De Blasi;  G. Pianigiani — 1992

Annales Polonici Mathematici

An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].

Continuous Selections in α-Convex Metric Spaces

F. S. De Blasi;  G. Pianigiani — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.

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