# American Institute of Mathematical Sciences

January  2018, 17(1): 163-175. doi: 10.3934/cpaa.2018010

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

 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  September 2017

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.

Citation: Alex H. Ardila. Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field. Communications on Pure & Applied Analysis, 2018, 17 (1) : 163-175. doi: 10.3934/cpaa.2018010
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