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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Continuous selection theorems

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2005
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tom 25
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nr 1
159-163
EN
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
2

Relaxation theorem for set-valued functions with decomposable values

88%
Kisielewicz A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1996
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tom 16
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nr 1
91-97
EN
Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has $fχ_A + gχ_{T\A} ∈ K$. Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
3
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Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

63%
Djebali S., Ouahab A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
|
tom 30
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nr 1
23-49
EN
In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
4
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Multi-valued superpositions

53%
Appell J., Thái N. H., De Pascale E., Zabreĭko P. P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.......................................................................................................... 5 1. Multifunctions and selections............................................................................... 7  1. Multifunctions and selections.................................................................. 7  2. Continuous multifunctions and selections........................................... 9  3. Measurable multifunctions and selections............................................ 16 2. Multifunctions of two variables............................................................................... 19  4. Carathéodory multifunctions and selections......................................... 19  5. The Scorza Dragoni property..................................................................... 25  6. Implicit function theorems......................................................................... 32 3. The superposition operator................................................................................... 33  7. The superposition operator in the space S........................................... 34  8. The superposition operator in ideal spaces......................................... 39  9. The superposition operator in the space C........................................... 47 4. Closures and convexifications.............................................................................. 49  10. Strong closures........................................................................................ 49  11. Convexifications....................................................................................... 52  12. Weak closures.......................................................................................... 56 5. Fixed points and integral inclusions..................................................................... 59  13. Fixed point theorems for multi-valued operators................................ 60  14. Hammerstein integral inclusions........................................................ 63  15. A reduction method................................................................................... 68 6. Applications............................................................................................................... 72  16. Applications to elliptic systems.............................................................. 72  17. Applications to nonlinear oscillations................................................. 75  18. Applications to relay problems.............................................................. 78 References.................................................................................................................... 81 Index of symbols........................................................................................................... 93 Index of terms................................................................................................................ 95
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