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Nonlinear Integral Equations in Abstract Spaces

  • Book
  • © 1996

Overview

Authors:
  1. Dajun Guo

    1. Shandong University, P. R. China

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  2. V. Lakshmikantham

    1. Department of Applied Mathematics, Florida Institute of Technology, Melbourne, USA

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  3. Xinzhi Liu

    1. University of Waterloo, Canada

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Part of the book series: Mathematics and Its Applications (MAIA, volume 373)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
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  2. Preliminaries

    • Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 1-52

  3. Nonlinear Integral Equations In Banach Spaces

    • Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 53-171

  4. Nonlinear Integro-Differential Equations in Banach Spaces

    • Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 173-239

  5. Nonlinear Impulsive Integral Equations in Banach Spaces

    • Dajun Guo, V. Lakshmikantham, Xinzhi Liu
    Pages 241-332

  6. Back Matter

    Pages 333-344
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Keywords

About this book

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.

Authors and Affiliations

  • Shandong University, P. R. China

    Dajun Guo

  • Department of Applied Mathematics, Florida Institute of Technology, Melbourne, USA

    V. Lakshmikantham

  • University of Waterloo, Canada

    Xinzhi Liu

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