Abstract
The asymptotic behavior of solutions to Schrödinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate are derived.
| Original language | English |
|---|---|
| Pages (from-to) | 3895-3956 |
| Number of pages | 62 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 32 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - Nov 2012 |
Keywords
- Hardy's inequality
- Quantum N-body problem
- Schrödinger operators
- Singular cylindrical potentials