Sum-sets of small upper density
Guillaume Bordes (2005)
Acta Arithmetica
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Guillaume Bordes (2005)
Acta Arithmetica
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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.
Ibrahim, A.G. (1998)
International Journal of Mathematics and Mathematical Sciences
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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.
O'Regan, Donal (1999)
Journal of Applied Mathematics and Stochastic Analysis
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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.
Rzepecka, Genowefa (2015-12-08T07:20:54Z)
Acta Universitatis Lodziensis. Folia Mathematica
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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.
James Foran (1977)
Colloquium Mathematicae
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Wilczyński, Władysław
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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.
David Lubell (1971)
Acta Arithmetica
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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.