On some aspects of oscillation theory and geometry

The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation we prove some new results in both directions, ranging from oscil...

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Bibliographic Details
Main Authors: Bianchini, Bruno, Mari, Luciano, Rigoli, Marco
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2013
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Difference equations
Differential equations, Elliptic
Oscillation theory
Spectral theory (Mathematics)
spectral theory
comparison
Oscillation
uncertainty principle
compactness
index
Schrodinger operator
immersions
ISBN:9780821887998, 0821887998
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary:The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation we prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE’s that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep our investigation basically self-contained we also collect some, more or less known, material which often appears in the literature in various forms and for which we give, in some instances, new proofs according to our specific point of view.
Bibliography:Volume 225, number 1056 (first of 4 numbers), September 2013
Includes bibliographical references (p. 187-195)
ISBN:9780821887998
0821887998
ISSN:0065-9266
1947-6221
DOI:10.1090/S0065-9266-2012-00681-2