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Some applications of the topological degree theory to multi-valued boundary value problems

Seria
Rozprawy Matematyczne tom/nr w serii: 229 wydano: 1984
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Warianty tytułu
Abstrakty
EN
CONTENTS
Introduction......................................................................................................5

I. Preliminaries
1. Strong convergence and weak convergence in Banach spaces..................7
2. Compact and weakly compact sets in Banach spaces.................................7
3. Weakly compact sets in the space of integrable functions...........................8
4. Compact sets in the space of continuous functions.....................................9
5. Basic integral and differential inequalities..................................................10

II. Multi-valued mappings
1. Upper semi-continuous, compact and weakly compact mappings..............12
2. L-compact mappings..................................................................................14
3. Caratheodory conditions for convex-valued mappings...............................17
4. Convex-valued, weakly compact selectors.................................................19
5. Compact convex-valued vector fields.........................................................20

III. Multi-valued boundary value problems
1. The degree of the boundary value problem...............................................21
2. Existence theorems....................................................................................23

IV. Boundary value problems for ordinary differential equations
1. Admissible boundary value problems associated with problem (IV.1).........27
2. Existence theorems....................................................................................29
3. First order problems...................................................................................31
4. Second order problems..............................................................................34

V. Boundary value problems for some hyperbolic partial differential equations
1. Multi-valued Darboux problem....................................................................36
2. A multi-valued problem with nonlinear boundary conditions.......................38

VI. Boundary value problems for elliptic partial differential equations
1. Basic function spaces................................................................................40
2. The general boundary value problem........................................................41

References ...................................................................................................44
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 229
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXXIX
Daty
wydano
1984
Twórcy
Bibliografia
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