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In this paper we study the behavior of solutions of a second orderdifferential equation. The existence of a zero and its localization allow us toget some compactness results. In particular we obtain a Myers' type theoremeven in the presence of an amount of negative curvature. The technique we usealso applies to the study of spectral properties of Schroedinger operators oncomplete manifolds.

Myers' type theorems and some related oscillation results