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

Veronica Felli; Elsa M. Marchini; Susanna Terracini

doi:10.3934/dcds.2008.21.91

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2008, Volume 21, Issue 1: 91-119. Doi: 10.3934/dcds.2008.21.91

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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
2.
Universitµa di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano

Received: November 30, 2006

Revised: March 31, 2007

Published: December 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J10, 35B40; Secondary: 35J60.

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