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Operator Theory: Advances and Applications

Floquet Theory for Partial Differential Equations

Authors: Kuchment, P.A.

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Softcover $84.99
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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].

Table of contents (6 chapters)

  • Holomorphic Fredholm Operator Functions

    Kuchment, Peter

    Pages 1-89

  • Spaces, Operators and Transformations

    Kuchment, Peter

    Pages 91-102

  • Floquet Theory for Hypoelliptic Equations and Systems in the Whole Space

    Kuchment, Peter

    Pages 103-123

  • Properties of Solutions of Periodic Equations

    Kuchment, Peter

    Pages 125-186

  • Evolution Equations

    Kuchment, Peter

    Pages 187-262

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-0348-8573-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-7643-2901-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.99
price for USA in USD
  • ISBN 978-3-0348-9686-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Floquet Theory for Partial Differential Equations
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
60
Copyright
1993
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-8573-7
DOI
10.1007/978-3-0348-8573-7
Hardcover ISBN
978-3-7643-2901-3
Softcover ISBN
978-3-0348-9686-3
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XIV, 354
Topics