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. © Mathematica Josephina, Inc. 2011.
Mastrolia, P., Rimoldi, M., Veronelli, G. (2012). Myers-type theorems and some related oscillation results. THE JOURNAL OF GEOMETRIC ANALYSIS, 22(3), 763-779 [10.1007/s12220-011-9213-0].
Myers-type theorems and some related oscillation results
RIMOLDI, MICHELE;Veronelli, G.
2012
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. © Mathematica Josephina, Inc. 2011.
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