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

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- by Ross G. Pinsky PDF
- Trans. Amer. Math. Soc.
**360**(2008), 6545-6554 Request permission

## Abstract:

Consider the equation \[ {(^*)\qquad \qquad \qquad \qquad \qquad \frac 12\Delta u-Vu=0 \text { in }R^d, \qquad \qquad \qquad \qquad \qquad \qquad }\] for $d\ge 3$. For certain classes of potentials $V$, 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.## References

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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
- Received by editor(s): June 26, 2006
- Received by editor(s) in revised form: January 16, 2007
- Published electronically: June 26, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 6545-6554 - MSC (2000): Primary 60H30, 35J10
- DOI: https://doi.org/10.1090/S0002-9947-08-04473-5
- MathSciNet review: 2434298