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Theory of a Higher-Order Sturm-Liouville Equation

  • Book
  • © 1997

Overview

Authors:
  1. Vladimir Kozlov
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  2. Vladimir Maz'ya
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1659)

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About this book

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Keywords

Table of contents (8 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Basic equation with constant coefficients

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 1-14

  3. The operator M(∂ t ) on a semiaxis and an interval

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 15-24

  4. The operator M(∂ t )−ω0 with constant ω0

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 25-35

  5. Green's function for the operator M(∂ t )−ω(t)

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 37-45

  6. Uniqueness and solvability properties of the operator M(∂ t −ω(t)

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 47-80

  7. Properties of M(∂ t −ω(t) under various assumptions about ω(t)

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 81-110

  8. Asymptotics of solutions at infinity

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 111-125

  9. Application to ordinary differential equations with operator coefficients

    • Vladimir Kozlov, Vladimir Maz'ya
    Pages 127-136

  10. Back Matter

    Pages 137-140
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Bibliographic Information

  • Book Title: Theory of a Higher-Order Sturm-Liouville Equation

  • Authors: Vladimir Kozlov, Vladimir Maz'ya

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094700

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63065-4Published: 17 July 1997

  • eBook ISBN: 978-3-540-69122-8Published: 13 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 144

  • Topics: Partial Differential Equations

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