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Methods in Nonlinear Integral Equations

  • Book
  • © 2002

Overview

Authors:
  1. Radu Precup

    1. Department of Applied Mathematics, Babeş-Bolyai University, Cluj, Romania

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Overview

    1. Overview

      • Radu Precup
      Pages 1-9

  3. Fixed Point Methods

    1. Front Matter

      Pages 11-11
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    2. Compactness in Metric Spaces

      • Radu Precup
      Pages 13-23

    3. Completely Continuous Operators on Banach Spaces

      • Radu Precup
      Pages 25-34

    4. Continuous Solutions of Integral Equations via Schauder’s Theorem

      • Radu Precup
      Pages 35-41

    5. The Leray-Schauder Principle and Applications

      • Radu Precup
      Pages 43-60

    6. Existence Theory in L p Spaces

      • Radu Precup
      Pages 61-76

  5. Iterative Methods

    1. Front Matter

      Pages 149-149
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    2. The Discrete Continuation Principle

      • Radu Precup
      Pages 151-162

    3. Monotone Iterative Methods

      • Radu Precup
      Pages 163-194

    4. Quadratically Convergent Methods

      • Radu Precup
      Pages 195-210

  6. Back Matter

    Pages 217-218
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Keywords

About this book

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

Reviews

From the reviews:

"This book deals with several methods of nonlinear analysis for the investigation of nonlinear integral equations … . Necessary abstract results of nonlinear analysis … are provided. … new points of view, extensions and applications are presented. … The presentation is self-contained and therefore should be useful to find the current ideas and methods." (V. Lakshmikantham, Zentralblatt MATH, Vol. 1060 (11), 2005)

Authors and Affiliations

  • Department of Applied Mathematics, Babeş-Bolyai University, Cluj, Romania

    Radu Precup

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