Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 275, Issue 1, Pages 108-130Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/S0022-247X(02)00278-0
Keywords
nonlinear Schrodinger equations; semiclassical limit; electromagnetic fields; complex-valued solutions
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We study the existence of standing waves for a class of nonlinear Schrodinger equations in R-n, with both an electric and a magnetic field. Under suitable non-degeneracy assumptions on the critical points of an auxiliary function related to the electric field, we prove the existence and the multiplicity of complex-valued solutions in the semiclassical limit. We show that, in the semiclassical limit, the presence of a magnetic field produces a phase in the complex wave, but it does not influence the location of peaks of the modulus of these waves. (C) 2002 Elsevier Science (USA). All rights reserved.
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