\(L_ p\)-continuous extreme selectors of multifunctions with decomposable values: Existence theorems

DOI10.1007/BF00425964zbMath0847.54019MaRDI QIDQ1915628

D. A. Tolstonogov, A. A. Tolstonogov

Publication date: 15 October 1996

Published in: Set-Valued Analysis (Search for Journal in Brave)

zbMATH Keywords

differential inclusionsmultifunctioncontinuous selectordecomposable set

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Selections in general topology (54C65) Ordinary differential inclusions (34A60)

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Cites Work

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• Differential inclusions with non-closed, non-convex right hand side
• Continuous selections. I
• Non-convex-valued differential inclusions in Banach spaces
• Nonlinear bang-bang principle in \({\mathbb{R}}^ n\)
• Differential inclusions in Banach spaces
• Geometry of Banach spaces. Selected topics
• Convex analysis and measurable multifunctions
• Integrals, conditional expectations, and martingales of multivalued functions
• A Baire category approach to the bang-bang property
• Geometric aspects of convex sets with the Radon-Nikodym property
• On total differential inclusions
• Continuous selections for a family of nonconvex-valued mappings with noncompact domain
• Sur certains espaces vectoriels topologiques
• Continuous selections for a class of non-convex multivalued maps
• Representation of Set Valued Operators
• Extensions and selections of maps with decomposable values
• On the density of extremal solutions of differential inclusions
• Measurable relations
• Extremal selections of multifunctions generating a continuous flow

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