On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity. (English) Zbl 1141.35362
Summary: Asymptotics of solutions to Schrödinger equations with singular dipole-type potentials are investigated. We evaluate the exact behavior near the singularity of solutions to elliptic equations with potentials which are purely angular multiples of radial inverse-square functions. Both the linear and the semilinear (critical and subcritical) cases are considered.
MSC:
35J10 | Schrödinger operator, Schrödinger equation |
35B40 | Asymptotic behavior of solutions to PDEs |
35J60 | Nonlinear elliptic equations |