Two-Point Boundary Value Problems: Lower and Upper Solutions

Colette De Coster and Patrick Habets (Eds.)044452200X, 9780444522009, 9780080462479

This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method · Construction of lower and upper solutions in problems · Working applications and illustrated theorems by examples · Description of the history of the method and Bibliographical notes

---

Table of contents :
Content:
Preface
Pages ix-x
Colette De Coster, Patrick Habets

Notations
Pages xi-xii

Introduction—The history
Pages 1-24

Chapter I The periodic problem Original Research Article
Pages 25-74

Chapter II The separated BVP Original Research Article
Pages 75-133

Chapter III Relation with degree theory Original Research Article
Pages 135-188

Chapter IV Variational methods Original Research Article
Pages 189-239

Chapter V Monotone iterative methods Original Research Article
Pages 241-277

Chapter VI Parametric multiplicity problems Original Research Article
Pages 279-314

Chapter VII Resonance and non-resonance Original Research Article
Pages 315-343

Chapter VIII Positive solutions Original Research Article
Pages 345-374

Chapter IX Problems with singular forces Original Research Article
Pages 375-404

Chapter X Singular perturbations Original Research Article
Pages 405-424

Chapter XI Bibliographical notes Original Research Article
Pages 425-434

Appendix
Pages 435-462

Bibliography
Pages 463-487

Index
Pages 488-489