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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

Veronica Felli 1, , Elsa M. Marchini 2, and  Susanna Terracini 1,

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.
Keywords: Hardy's inequality, dipole moment, Singular potentials, Schrödinger operators..
Mathematics Subject Classification: Primary: 35J10, 35B40; Secondary: 35J6.
Citation: Veronica Felli, Elsa M. Marchini, Susanna Terracini. On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 91-119. doi: 10.3934/dcds.2008.21.91
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