Displaying similar documents to “On the density of extremal solutions of differential inclusions”

Evolution inclusions in non separable Banach spaces

Francesco Saverio De Blasi, Giulio Pianigiani (1999)

Commentationes Mathematicae Universitatis Carolinae

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We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Strong proximinality and polyhedral spaces.

Gilles Godefroy, V. Indumathi (2001)

Revista Matemática Complutense

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In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.

Some existence results for solutions of differential inclusions with retardations

L. H. Erbe, W. Krawcewicz, Shaozhu Chen (1991)

Annales Polonici Mathematici

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Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.