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Existence Theory for Nonlinear Integral and Integrodifferential Equations

  • Book
  • © 1998

Overview

Authors:
  1. Donal O’Regan

    1. Department of Mathematics, National University of Ireland, Galway, Ireland

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    You can also search for this author in PubMed   Google Scholar

  2. Maria Meehan

    1. Department of Mathematics, National University of Ireland, Galway, Ireland

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 445)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction and Preliminaries

    • Donal O’Regan, Maria Meehan
    Pages 1-13

  3. Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations

    • Donal O’Regan, Maria Meehan
    Pages 14-36

  4. Solution Sets of Abstract Volterra Equations

    • Donal O’Regan, Maria Meehan
    Pages 37-45

  5. Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Compact Intervals

    • Donal O’Regan, Maria Meehan
    Pages 46-64

  6. Existence Theory for Nonlinear Fredholm and Volterra Integral Equations on Half-Open Intervals

    • Donal O’Regan, Maria Meehan
    Pages 65-108

  7. Existence Theory for Nonlinear Nonresonant Operator and Integral Equations

    • Donal O’Regan, Maria Meehan
    Pages 109-127

  8. Existence Theory for Nonlinear Resonant Operator and Integral Equations

    • Donal O’Regan, Maria Meehan
    Pages 128-143

  9. Integral Inclusions

    • Donal O’Regan, Maria Meehan
    Pages 144-156

  10. Approximation of Solutions of Operator Equations on the Half Line

    • Donal O’Regan, Maria Meehan
    Pages 157-175

  11. Operator Equations in Banach Spaces Relative to the Weak Topology

    • Donal O’Regan, Maria Meehan
    Pages 176-190

  12. Stochastic Integral Equations

    • Donal O’Regan, Maria Meehan
    Pages 191-203

  13. Periodic Solutions for Operator Equations

    • Donal O’Regan, Maria Meehan
    Pages 204-215

  14. Back Matter

    Pages 216-218
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Keywords

About this book

The theory of integral and integrodifferential equations has ad­ vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono­ graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap­ ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in­ tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the­ ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur­ ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte­ gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.

Authors and Affiliations

  • Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan, Maria Meehan

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