A probabilistic approach to bounded/positive solutions for Schrödinger operators with certain classes of potentials

Author:
Ross G. Pinsky

Journal:
Trans. Amer. Math. Soc. **360** (2008), 6545-6554

MSC (2000):
Primary 60H30, 35J10

Published electronically:
June 26, 2008

MathSciNet review:
2434298

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider the equation

for . For certain classes of potentials , we use probabilistic tools to study the bounded solutions and the positive solutions for (*). A primary motivation is to offer probabilistic intuition for the results.

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Additional Information

**Ross G. Pinsky**

Affiliation:
Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

Email:
pinsky@math.technion.ac.il

DOI:
https://doi.org/10.1090/S0002-9947-08-04473-5

Keywords:
Liouville theorem,
bounded solutions,
positive solutions,
Schr\"odinger equation

Received by editor(s):
June 26, 2006

Received by editor(s) in revised form:
January 16, 2007

Published electronically:
June 26, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

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