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Oscillation Theory of Two-Term Differential Equations : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Uri Elias

Oscillation Theory of Two-Term Differential Equations


By: Uri Elias

Hardcover Published: 31st March 1997
ISBN: 9780792344476
Number Of Pages: 226

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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.

The Basic Lemma
Boundary Value Functions
Bases of Solutions
Comparison of Boundary Value Problems
Comparison Theorems for Two Equations
Disfocality and Its Characterization
Various Types of Disfocality
Solutions on an Infinite Interval
Disconjugacy and its Characterization
Eigenvalue Problems
More Extremal Points
Minors of the Wronskian
The Dominance Property of Solutions
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792344476
ISBN-10: 0792344472
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 226
Published: 31st March 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 1.91
Weight (kg): 0.57