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Oscillation Theory of Two-Term Differential Equations

  • Book
  • © 1997


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

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About this book

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 propĀ­ 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.

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Table of contents (15 chapters)

Authors and Affiliations

  • Department of Mathematics, Technion Israel Institute of Technology, Haifa, Israel

    Uri Elias

Bibliographic Information

  • Book Title: Oscillation Theory of Two-Term Differential Equations

  • Authors: Uri Elias

  • Series Title: Mathematics and Its Applications

  • DOI:

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1997

  • Hardcover ISBN: 978-0-7923-4447-6Published: 31 March 1997

  • Softcover ISBN: 978-90-481-4806-6Published: 07 December 2010

  • eBook ISBN: 978-94-017-2517-0Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: VII, 226

  • Topics: Ordinary Differential Equations

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