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On Some Aspects of Oscillation Theory and Geometry
 
Bruno Bianchini Universita Degli Studi Di Padova, Padova, Italy
Luciano Mari Universidade Federal Do Ceara, Fortaleza, Brazil
Marco Rigoli University degli Studi di Milano, Milano, Italy
On Some Aspects of Oscillation Theory and Geometry
eBook ISBN:  978-1-4704-1056-8
Product Code:  MEMO/225/1056.E
List Price: $86.00
MAA Member Price: $77.40
AMS Member Price: $68.80
On Some Aspects of Oscillation Theory and Geometry
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On Some Aspects of Oscillation Theory and Geometry
Bruno Bianchini Universita Degli Studi Di Padova, Padova, Italy
Luciano Mari Universidade Federal Do Ceara, Fortaleza, Brazil
Marco Rigoli University degli Studi di Milano, Milano, Italy
eBook ISBN:  978-1-4704-1056-8
Product Code:  MEMO/225/1056.E
List Price: $86.00
MAA Member Price: $77.40
AMS Member Price: $68.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2252013; 195 pp
    MSC: Primary 34; 58; 35; Secondary 53; 57;

    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 the authors 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 their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The Geometric setting
    • 3. Some geometric examples related to oscillation theory
    • 4. On the solutions of the ODE $(vz’)’+Avz=0$
    • 5. Below the critical curve
    • 6. Exceeding the critical curve
    • 7. Much above the critical curve
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2252013; 195 pp
MSC: Primary 34; 58; 35; Secondary 53; 57;

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 the authors 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 their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

  • Chapters
  • 1. Introduction
  • 2. The Geometric setting
  • 3. Some geometric examples related to oscillation theory
  • 4. On the solutions of the ODE $(vz’)’+Avz=0$
  • 5. Below the critical curve
  • 6. Exceeding the critical curve
  • 7. Much above the critical curve
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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