Two-Point Boundary Value Problems: Lower and Upper Solutions

Two-Point Boundary Value Problems: Lower and Upper Solutions

by C. De Coster, Patrick Habets
     
 

ISBN-10: 044452200X

ISBN-13: 9780444522009

Pub. Date: 06/28/2006

Publisher: Elsevier Science

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

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Overview

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

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Product Details

ISBN-13:
9780444522009
Publisher:
Elsevier Science
Publication date:
06/28/2006
Series:
Mathematics in Science and Engineering Series, #205
Pages:
502
Product dimensions:
1.06(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface
Notations
Introduction - The History
I. The Periodic Problem
II. The Separated BVP
III. Relation with Degree Theory
IV. Variational Methods
V. Monotone Iterative Methods
VI. Parametric Multiplicity Problems
VII. Resonance and Nonresonance
VIII. Positive Solutions
IX. Problem with Singular Forces
X. Singular Perturbations
XI. Bibliographical Notes
Appendix
Bibliography
Index

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