Breathing modes  for the Schrödinger-Poisson system with a multiple--well external potential

Margherita Nolasco

doi:10.3934/cpaa.2010.9.1411

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2010, Volume 9, Issue 5: 1411-1419. Doi: 10.3934/cpaa.2010.9.1411

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Breathing modes for the Schrödinger-Poisson system with a multiple--well external potential

Margherita Nolasco^1,

1.
Dipartimento di Matematica Pura ed Applicata, Università di L’Aquila, Via Vetoio, Coppito, 67010 L’Aquila

Received: July 31, 2009

Revised: December 31, 2009

Published: August 2010

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Abstract

We consider a Schrödinger-Poisson system with attractive selfinteractions and a multiple well external potential. We prove the existence of multiple breathing mode solutions bifurcating from the Hartree ground state.

Keywords:

Schrödinger-Poisson equation,
nonlinear elliptic equations.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35J10.

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