Abstract
The first aim in this paper is to deal with asymptotic behaviors of Green-Sch potentials in a cylinder. As an application we prove the integral representation of nonnegative weak solutions of the stationary Schrödinger equation in a cylinder. Next we give asymptotic behaviors of them outside an exceptional set. Finally we obtain a quantitative property of rarefied sets with respect to the stationary Schrödinger operator at +∞ in a cylinder. Meanwhile we show that the reverse of this property is not true.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2321-2338 |
| Number of pages | 18 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 22 |
| Issue number | 6 |
| DOIs | |
| State | Published - Aug 2017 |
Keywords
- Asymptotic behavior
- Green-Sch potential
- Stationary Schrödinger operator
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics