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

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  • 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.

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


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