, Volume 22, Issue 3, pp 763-779
Date: 25 Jan 2011

Myers-Type Theorems and Some Related Oscillation Results

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Abstract

In this paper we study the behavior of solutions of a second-order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers-type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the study of spectral properties of Schrödinger operators on complete manifolds.

Communicated by Marco M. Peloso.