Eigenvalues of Schrödinger operators with potential asymptotically homogeneous of degree

Authors:
Andrew Hassell and Simon Marshall

Journal:
Trans. Amer. Math. Soc. **360** (2008), 4145-4167

MSC (2000):
Primary 35P20

DOI:
https://doi.org/10.1090/S0002-9947-08-04479-6

Published electronically:
March 13, 2008

MathSciNet review:
2395167

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Abstract | References | Similar Articles | Additional Information

Abstract: We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function , the number of bound states of the operator in below . Here is a bounded potential behaving asymptotically like where is a function on the sphere. It is well known that the eigenvalues of such an operator are all nonpositive, and accumulate only at 0. If the operator on the sphere has negative eigenvalues less than , we prove that may be estimated as

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Additional Information

**Andrew Hassell**

Affiliation:
Department of Mathematics, The Australian National University, ACT 0200, Australia

Email:
hassell@maths.anu.edu.au

**Simon Marshall**

Affiliation:
Department of Mathematics, The University of Auckland, Auckland 1142, New Zea-land

Address at time of publication:
Department of Mathematics, Fine Hall, Princeton University, Washington Rd., Princeton, New Jersey 08544

Email:
slm@math.princeton.edu

DOI:
https://doi.org/10.1090/S0002-9947-08-04479-6

Received by editor(s):
June 8, 2006

Published electronically:
March 13, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.