Displaying similar documents to “Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side”

D sets and IP rich sets in ℤ

Randall McCutcheon, Jee Zhou (2016)

Fundamenta Mathematicae

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We give combinatorial characterizations of IP rich sets (IP sets that remain IP upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultrafilters, all of whose members have positive upper Banach density) in ℤ. We then show that the family of IP rich sets strictly contains the family of D sets.

Second-order viability result in Banach spaces

Myelkebir Aitalioubrahim, Said Sajid (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.

Lower semicontinuous differential inclusions

Tzanko Donchev (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

Mouffak Benchohra (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.

A note on uniform or Banach density

Georges Grekos, Vladimír Toma, Jana Tomanová (2010)

Annales mathématiques Blaise Pascal

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In this note we present and comment three equivalent definitions of the so called or density of a set of positive integers.

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.