Singular Differential and Integral Equations with Applications

  • Ravi P. Agarwal
  • Donal O’Regan

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ravi P. Agarwal, Donal O’Regan
    Pages 1-143
  3. Ravi P. Agarwal, Donal O’Regan
    Pages 144-297
  4. Ravi P. Agarwal, Donal O’Regan
    Pages 298-336
  5. Back Matter
    Pages 337-402

About this book

Introduction

In the last century many problems which arose in the science, engineer­ ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ­ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis­ tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono­ graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.

Keywords

Boundary value problem Integral equation differential equation ordinary differential equation

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-3004-4
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6356-4
  • Online ISBN 978-94-017-3004-4
  • About this book
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