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

Pruszko, Tadeusz

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

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Tadeusz Pruszko

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Rozprawy Matematyczne tom/nr w serii: 229 wydano: 1984

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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

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Instytut Matematyczny Polskiej Akademii Nauk

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Warszawa

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Rozprawy Matematyczne tom/nr w serii: 229

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48

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Dissertationes Mathematicae, Tom CCXXIX

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wydano

1984

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autor

Tadeusz Pruszko

Bibliografia

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

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