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Nonlinear boundary value problems for ordinary differential equations

Seria
Rozprawy Matematyczne tom/nr w serii: 244 wydano: 1985
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Warianty tytułu
Abstrakty
EN
Comments
This tract is intended to be accessible to a broad spectrum of readers. Those with out much previous experience with differential equations might find it profitable (when the need arises) to consult one of the following standard texts: Coddington-Levinson [17], Hale [35], Hartman [38], Mawhin-Rouche [61]. The bibliography given below is restricted mostly to the problems discussed in the tract or closely related topics. A small number of additional references are included however in order to provide a guide to further study; most of these contain extensive bibliographies for the material they cover. The following references include some of the recent surveys and monographs that are related to the subject matter of this tract in a substantial way: Bailey-Shampine-Waltman [7], Bernfeld-Lakshmikantahm [11], Cesari [15], Eloe-Henderson [21], Gaines-Mawhin [25], Gudkov-Klokow-Lepin-Ponomarov [34], Jackson [43], Keller [47], Lefschetz [57], Mawhin [60], Protter-Weinberger [69].
EN

CONTENTS
Comments............................................................................................................................5
CHAPTER I
Introduction
§ 1. Elementary theory of second order differential equations...........................................12
§ 2. Topological preliminaries.............................................................................................14
§ 3. The maximum principle................................................................................................16
§ 4. Existence and a priori bounds-examples.....................................................................19
§ 5. Problems with other boundary conditions....................................................................25
CHAPTER II
The Bernstein theory of the equation y" = f(t, y, y')
§ 1. The homogeneous Dirichlet, Neumann, and periodic problems...................................28
§ 2. The homogeneous Sturm-Liouville problem................................................................34
§ 3. Inhomogeneous boundary conditions..........................................................................35
§ 4. Examples and remarks................................................................................................39
§ 5. Bernstein-Nagumo growth conditions..........................................................................44
§ 6. Nonlinear boundary conditions....................................................................................50
§ 7. Uniqueness..................................................................................................................52
CHAPTER III
Applications
§ 1. Steady-state temperature distributions........................................................................56
§ 2. The Thomas-Fermi problem........................................................................................59
§ 3. Singular boundary value problems..............................................................................62
§ 4. Osmotic flow.................................................................................................................64
§ 5. Positive solutions to diffusion equations......................................................................70
CHAPTER IV
Other second order boundary value problems
§ 1. Periodic solutions to differential equations of Nirenberg type......................................76
§ 2. The Dirichlet problem for y" = f(y') and the Neumann problem for y" = f(t,y,y').............85
§ 3. Upper and lower solutions...........................................................................................94
CHAPTER V
Even order systems and higher order equations
§ 1. General existence theorems........................................................................................99
§ 2. Second order systems...............................................................................................102
§ 3. Third and fourth order problems................................................................................108
§ 4. Higher even order equations......................................................................................111
CHAPTER VI
Numerical solution of boundary value problems
§ 1. Newton’s method........................................................................................................113
§ 2. The shooting method for the Dirichlet problem..........................................................115
§ 3. The shooting method for the Neumann problem........................................................120
§ 4. Quasilinearization for boundary value problems........................................................121
References.......................................................................................................................125
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 244
Liczba stron
128
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXLIV
Daty
wydano
1985
Twórcy
Bibliografia
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