The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

Author:
Zhongwei Shen

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3447-3456

MSC (2000):
Primary 35P20, 35J10

DOI:
https://doi.org/10.1090/S0002-9939-03-06968-5

Published electronically:
February 20, 2003

MathSciNet review:
1990634

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a noncompact complete Riemannian manifold. We consider the Schrödinger operator acting on , where is a nonnegative, locally integrable function on . We obtain some simple conditions which imply that , the bottom of the spectrum of , is strictly positive. We also establish upper and lower bounds for the counting function .

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Additional Information

**Zhongwei Shen**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Email:
shenz@ms.uky.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-06968-5

Received by editor(s):
May 27, 2002

Published electronically:
February 20, 2003

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2003
American Mathematical Society