Nonlinear Schrödinger equation with bounded magnetic field

2019/11/05 by Devillanova, Giuseppe, Tintarev, Cyril
#35J20 #35J61 #35Q40 #35Q60 #46B50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.01657

Abstract

The paper studies existence of solutions for the nonlinear Schrödinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space.

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