Includes bibliographical references (pages 187-195) and index.
Introduction The geometric setting Some geometric examples related to oscillation theory On the solutions of the ODE $(vz')' Avz=0$ Below the critical curve Exceeding the critical curve Much above the critical curve Bibliography.
(source: Nielsen Book Data)
The aim of this paper is to analyse 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. (source: Nielsen Book Data)