Nonlinear Two Point Boundary Value Problems

Paul B. Bailey, Lawrence F. Shampine and Paul E. Waltman (Eds.)9780120733507, 0120733501

The purpose of this book is to describe as simply as possible a number of the ideas and methods which seem to be particularly helpful in the study of nonlinear boundary value problems for differential equations of the second order. Apart from the restriction to second order, the kinds of equations treated and the level of treatment are those common to introductory courses in differential equations which treat initial value problems. The reason for this restriction is that whereas nth order initial value problems are not essentially more difficult than first or second order, higher order boundary value problems are. Those of second order already show the difficulties but are becoming fairly well understood. Much of the material has only recently appeared in the mathematical literature, however, and cannot yet be found in the textbooks.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Pages vii-ix

Chapter 1 Introduction
Pages 1-16

Chapter 2 Relations between the First and Second Boundary Value Problems
Pages 17-20

Chapter 3 Picard’s Iteration
Pages 21-49

Chapter 4 The Distance between Zeros and the Uniqueness Interval
Pages 50-69

Chapter 5 Comparison Theorems
Pages 70-87

Chapter 6 Principal Existence Theorems
Pages 88-102

Chapter 7 Further Existence and Uniqueness Results
Pages 103-127

Chapter 8 Numerical Solution by Initial Value Methods
Pages 128-140

Chapter 9 Numerical Solution by Boundary Value Methods
Pages 141-167

Index
Pages 169-171