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• # Książka - szczegóły

Tytuł książki

## Some functional differential equations

### Seria

Rozprawy Matematyczne tom/nr w serii: 100 wydano: 1973

### Abstrakty

EN

CONTENTS
Introduction............................................................................................................................................................................... 5
Chapter 0. PRELIMINARIES
0.1. (Preliminary remarks and notation)............................................................................................................................. 9
0.2. (Notation — continuation).............................................................................................................................................. 10
0.3. (Notation and some definitions).................................................................................................................................. 10
0.4. (Statement of problems; definition of solutions of differential functional equations)......................................... 12
0.5. (Equivalence of problems: differential and integral; definition of solutions of integral equations).................. 14
Chapter I. EXISTENCE AND UNIQUENESS OF SOLUTIONS AND THE CONVERGENCE OF SUCCESSIVE
APPROXIMATIONS IN COMPACT SETS
1.1. Notation and definitions................................................................................................................................................. 17
1.2. Uniqueness...................................................................................................................................................................... 18
1.3. Existence and successive approximations................................................................................................................ 19
1.4. Existence without uniqueness...................................................................................................................................... 22
1.5. Some generalizations of the results from 1.2-1.4..................................................................................................... 23
1.6. Some supplementary remarks..................................................................................................................................... 24
Chapter II. LOCAL AND GLOBAL EXISTENCE AND UNIQUENESS
2.1. Notation and definitions................................................................................................................................................. 27
2.2. Union of solutions........................................................................................................................................................... 28
2.3. Global uniqueness.......................................................................................................................................................... 29
2.4. Definition of the condition (W) and some remarks................................................................................................... 31
2.6. Local existence of solutions.......................................................................................................................................... 32
2.6. Lemmas............................................................................................................................................................................ 33
2.7. Limits of solutions on the boundary............................................................................................................................. 36
2.8. Prolongations................................................................................................................................................................... 38
2.9. Global existence under the assumptions on uniqueness...................................................................................... 39
2.10. Global existence without uniqueness....................................................................................................................... 41
2.11. Global existence without uniqueness by the method of A. Bielecki, T. Dłotko and M. Kuczma...................... 43
2.12. Existence of solutions under the assumptions (Y) and (Ỹ)................................................................................... 46
2.13. Local convergence of successive approximations under the assumptions (V)............................................... 47
2.14. Remarks on some generalizations........................................................................................................................... 49
Chapter III. CONTINUOUS DEPENDENCE OF SOLUTIONS ON GIVEN FUNCTIONS
3.1. Continuous dependence on $λ, ψ, {φ^a}$............................................ 51
3.2. Continuous dependence on ƒ....................................................... 52

Warszawa

### Seria

Rozprawy Matematyczne tom/nr w serii: 100

110

### Opis fizyczny

Dissertationes Mathematicae, Tom C

wydano
1973

autor

### Bibliografia

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