Nonlinear boundary value problems for ordinary differential equations

Granas, Andrzej; Guenther, Ronald; Lee, John

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Nonlinear boundary value problems for ordinary differential equations

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Andrzej Granas Ronald Guenther John Lee

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Rozprawy Matematyczne tom/nr w serii: 244 wydano: 1985

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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

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 244

Liczba stron

128

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Opis fizyczny

Dissertationes Mathematicae, Tom CCXLIV

Daty

wydano

1985

Twórcy

autor

Andrzej Granas

autor

Ronald Guenther

autor

John Lee

Bibliografia

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Nonlinear boundary value problems for ordinary differential equations

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