Nonlinear Integral Equations in Abstract Spaces

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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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.

• Integral equation
• banach spaces
• development
• equation
• integral
• mathematics
• online
• presentation
• ordinary differential equations

• 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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