Nonlinear Schrodinger equation with bounded magnetic field

[摘要] The paper studies existence of solutions for the nonlinear Schrodinger equation - (del+iA(x))(2)u + V (x)u = f (vertical bar u vertical bar)u (0.1) 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. (c) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-05

[关键词] Schrodinger operator;Magnetic field;Ground state;Concentration compactness;Profile decomposition;Critical points