Table of contents

  1. Front Matter
    Pages i-viii
  2. Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 1-52
  3. Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 53-171
  4. Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 173-239
  5. Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 241-332
  6. Back Matter
    Pages 333-344

About this book

Introduction

Many problems arising in the physical sciences, engineering, biology and ap­ plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab­ stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin­ ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica­ equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica­ tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul­ sive differential equations in Banach spaces.

Keywords

Integral equation banach spaces development equation integral mathematics online presentation

Authors and affiliations

  • Dajun Guo
    • 1
  • V. Lakshmikantham
    • 2
  • Xinzhi Liu
    • 3
  1. 1.Shandong UniversityP. R. China
  2. 2.Department of Applied MathematicsFlorida Institute of TechnologyMelbourneUSA
  3. 3.University of WaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-1281-9
  • Copyright Information Springer-Verlag US 1996
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8547-2
  • Online ISBN 978-1-4613-1281-9
  • About this book