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Floquet Theory for Partial Differential Equations

  • Book
  • © 1993

Overview

Authors:
  1. Peter Kuchment

    1. Department of Mathematics and Statistics, Wichita State University, Wichita, USA

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 60)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Holomorphic Fredholm Operator Functions

    • Peter Kuchment
    Pages 1-89

  3. Spaces, Operators and Transformations

    • Peter Kuchment
    Pages 91-102

  4. Floquet Theory for Hypoelliptic Equations and Systems in the Whole Space

    • Peter Kuchment
    Pages 103-123

  5. Properties of Solutions of Periodic Equations

    • Peter Kuchment
    Pages 125-186

  6. Evolution Equations

    • Peter Kuchment
    Pages 187-262

  7. Other Classes of Problems

    • Peter Kuchment
    Pages 263-302

  8. Back Matter

    Pages 303-354
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Keywords

About this book

Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111­ 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103­ 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

Authors and Affiliations

  • Department of Mathematics and Statistics, Wichita State University, Wichita, USA

    Peter Kuchment

Bibliographic Information

  • Book Title: Floquet Theory for Partial Differential Equations

  • Authors: Peter Kuchment

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8573-7

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1993

  • Hardcover ISBN: 978-3-7643-2901-3Published: 01 July 1993

  • Softcover ISBN: 978-3-0348-9686-3Published: 28 September 2012

  • eBook ISBN: 978-3-0348-8573-7Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIV, 354

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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