January  2008, 21(1): 91-119. doi: 10.3934/dcds.2008.21.91

On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity

1. 

Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano, Italy, Italy

2. 

Universitµa di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano, Italy

Received  December 2006 Revised  April 2007 Published  February 2008

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.
Citation: Veronica Felli, Elsa M. Marchini, Susanna Terracini. On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 91-119. doi: 10.3934/dcds.2008.21.91
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