Oscillation Theory of Two-Term Differential Equations

  • Uri Elias

Part of the Mathematics and Its Applications book series (MAIA, volume 396)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Uri Elias
    Pages 1-10
  3. Uri Elias
    Pages 11-26
  4. Uri Elias
    Pages 27-41
  5. Uri Elias
    Pages 42-48
  6. Uri Elias
    Pages 67-97
  7. Uri Elias
    Pages 98-110
  8. Uri Elias
    Pages 111-130
  9. Uri Elias
    Pages 131-140
  10. Uri Elias
    Pages 141-160
  11. Uri Elias
    Pages 161-175
  12. Uri Elias
    Pages 176-192
  13. Uri Elias
    Pages 193-207
  14. Uri Elias
    Pages 209-216
  15. Back Matter
    Pages 217-226

About this book

Introduction

Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop­ erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.

Keywords

Boundary value problem DEX Finite Lemma Natural boundary element method character differential equation eigenvalue problem equation extrema function functions operator theorem

Authors and affiliations

  • Uri Elias
    • 1
  1. 1.Department of MathematicsTechnion Israel Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2517-0
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4806-6
  • Online ISBN 978-94-017-2517-0
  • About this book
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