Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field

Alex H. Ardila

doi:10.3934/cpaa.2018010

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2018, Volume 17, Issue 1: 163-175. Doi: 10.3934/cpaa.2018010

This issue Previous Article Nonlinear SchrÖdinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities Next Article Time decay in dual-phase-lag thermoelasticity: Critical case

Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field

Alex H. Ardila

Instituto Nacional de Matemática Pura e Aplicada -IMPA Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, RJ, Brazil

Received: February 2017

Revised: June 2017

Published: January 2018

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Abstract

In this paper we study the existence and orbital stability of ground states for logarithmic Schrödinger equation under a constant magnetic field. For this purpose we establish the well-posedness of the Cauchy Problem in a magnetic Sobolev space and an appropriate Orlicz space. Then we show the existence of ground state solutions via a constrained minimization on the Nehari manifold. We also show that the ground state is orbitally stable.

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Mathematics Subject Classification: Primary:35Q55, 35Q51, 35B35.

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