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Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

  • Book
  • © 1999

Overview

Authors:
  1. Vladimir Kozlov

    1. Department of Mathematics, Linköping University, Linköping, Sweden

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    You can also search for this author in PubMed   Google Scholar

  2. Vladimir Maz’ya

    1. Department of Mathematics, Linköping University, Linköping, Sweden

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XX
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  2. Differential Equations with Constant Operator Coefficients

    1. Front Matter

      Pages 1-1
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    2. Power-Exponential Zeros

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 3-25

    3. Differential Operator Equations in Weighted Sobolev Spaces

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 27-48

    4. Solutions in a Local Sobolev Space

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 49-74

    5. Two-Weight L 2-Estimates

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 75-87

  3. Differential Equations with Variable Operator Coefficients

    1. Front Matter

      Pages 89-89
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    2. Existence, Uniqueness and “Pointwise” Estimates

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 91-112

    3. Corollaries of Previous Results Under Special Assumptions on L(t, D t )

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 113-131

    4. Two-Weight L 2-Estimates for Equations with Variable Coefficients

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 133-146

    5. Connection of Solutions Corresponding to Different Strips

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 147-164

    6. Applications to the Case of Perturbations Vanishing at Infinity

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 165-180

    7. Variants and Extensions of the Previous Theory

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 181-241

  4. Asymptotic Theory of Operator Differential Equations

    1. Front Matter

      Pages 243-243
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    2. Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(D t )

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 245-263

    3. Reduction to a First Order System

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 265-283

    4. General Asymptotic Representation

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 285-315

    5. Power-Exponential Asymptotics

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 317-344

    6. The Case of One Simple Eigenvalue on the Line

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 345-367

    7. Several Simple Eigenvalues on the Line

      • Vladimir Kozlov, Vladimir Maz’ya
      Pages 369-383
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Keywords

Reviews

From the reviews of the first edition:

"The book under review is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space … . this is an excellent book, that contains recent results of the topic, deep theoretical results and various applications to PDE-s. It is warmly recommended to specialists in ODE-s, PDE-s, functional analysis." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 72, 2006)

Authors and Affiliations

  • Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Kozlov, Vladimir Maz’ya

Bibliographic Information

  • Book Title: Differential Equations with Operator Coefficients

  • Book Subtitle: with Applications to Boundary Value Problems for Partial Differential Equations

  • Authors: Vladimir Kozlov, Vladimir Maz’ya

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-11555-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Hardcover ISBN: 978-3-540-65119-2Published: 19 January 1999

  • Softcover ISBN: 978-3-642-08453-9Published: 07 December 2010

  • eBook ISBN: 978-3-662-11555-8Published: 18 April 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XX, 444

  • Topics: Ordinary Differential Equations

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