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  • © 2023

Linear and Nonlinear Non-Fredholm Operators

Theory and Applications

Authors:

  1. Messoud Efendiev

    1. Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany

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  • Presents both linear and nonlinear non-Fredholm operators not systematically studied in usual mathematical literature

  • Describes higher-order models leading to non-Fredholm elliptic operators and their explicit solvability conditions

  • Discusses local vs nonlocal diffusion non-Fredholm elliptic equations and their well-posedness

  • 423 Accesses

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eBook USD 109.00
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  • ISBN: 978-981-19-9880-5
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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiv
    PDF

  2. Auxiliary Materials

    • Messoud Efendiev
    Pages 1-57

  6. Non-Fredholm Schrödinger type operators

    • Messoud Efendiev
    Pages 177-201

  7. Back Matter

    Pages 203-208
    PDF
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About this book

This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics.

First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood.

Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.
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Keywords

  • non-Fredholm, solvability, super diffusion, drift
  • Fourier harmonics, essential spectrum, nonlocal
  • higher order model, non-Fredholm Schrödinger type
  • mixed diffusion, essential spectrum, fixed point
  • convergence in the sense of sequences
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Authors and Affiliations

  • Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany

    Messoud Efendiev

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About the author


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Bibliographic Information

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Access via your institution
eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-981-19-9880-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 149.99
Price excludes VAT (USA)
Learn about institutional subscriptions