On some aspects of oscillation theory and geometry / Bruno Bianchini, Luciano Mari, Marco Rigoli
Type de document : MonographieCollection : Memoirs of the American Mathematical Society, 1056Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 2013Description : 1 vol. (V-195 p.) ; 26 cmISBN: 9780821887998.ISSN: 0065-9266.Bibliographie : Bibliogr. p. 187-195.Sujet MSC : 34C10, Qualitative theory for ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory53C21, Global differential geometry, Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58C40, Global analysis, analysis on manifolds, Spectral theory; eigenvalue problems on manifolds
35J10, PDEs - Elliptic equations and elliptic systems, Schrödinger operator, Schrödinger equation
57R42, Manifolds and cell complexes, Immersions in differential topologyEn-ligne : MathSciNet
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries AMS (Browse shelf(Opens below)) | Available | 12347-01 |
Bibliogr. p. 187-195
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.
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