Two-Point Boundary Value Problems: Lower and Upper Solutions

by C. De Coster, P. Habets

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.

Product Details

ISBN-13:	9780444522009
Publisher:	Elsevier Science
Publication date:	06/14/2006
Series:	Mathematics in Science and Engineering , #205
Edition description:	New Edition
Pages:	502
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

PrefaceNotationsIntroduction - The HistoryI. The Periodic ProblemII. The Separated BVPIII. Relation with Degree TheoryIV. Variational MethodsV. Monotone Iterative MethodsVI. Parametric Multiplicity ProblemsVII. Resonance and NonresonanceVIII. Positive SolutionsIX. Problem with Singular ForcesX. Singular PerturbationsXI. Bibliographical NotesAppendixBibliographyIndex

Editorial Reviews

"In this excellent monograph the authors present a survey of classical and recent results in the theory of lower and upper solutions applied to two-point boundary value problems...essential for researchers in this field." —Zentralblatt MATH, Two-Point Boundary Value Problems: Lower and Upper Solutions

From the Publisher