Infinite Interval Problems for Differential, Difference and Integral Equations

  • Ravi P. Agarwal
  • Donal O’Regan

Table of contents

  1. Front Matter
    Pages i-x
  2. Ravi P. Agarwal, Donal O’Regan
    Pages 1-89
  3. Ravi P. Agarwal, Donal O’Regan
    Pages 90-109
  4. Ravi P. Agarwal, Donal O’Regan
    Pages 110-138
  5. Ravi P. Agarwal, Donal O’Regan
    Pages 139-232
  6. Ravi P. Agarwal, Donal O’Regan
    Pages 233-276
  7. Ravi P. Agarwal, Donal O’Regan
    Pages 277-293
  8. Ravi P. Agarwal, Donal O’Regan
    Pages 294-328
  9. Ravi P. Agarwal, Donal O’Regan
    Pages 329-338
  10. Back Matter
    Pages 339-341

About this book

Introduction

Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom­ ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

Keywords

Boundary value problem DEX Finite Integral equation banach spaces development eXist equation integral mathematics time

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Donal O’Regan
    • 2
  1. 1.National University of SingaporeSingaporeRepublic of Singapore
  2. 2.University of IrelandGalwayIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-0718-4
  • Copyright Information Kluwer Academic Publishers 2001
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-3834-8
  • Online ISBN 978-94-010-0718-4
  • About this book
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