We study the existence of standing waves for a class of nonlinear Schrödinger equations in ℝn, 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. © 2002 Elsevier Science (USA). All rights reserved.

Cingolani, S., Secchi, S. (2002). Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 275(1), 108-130 [10.1016/S0022-247X(02)00278-0].

Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields

SECCHI, SIMONE
2002

Abstract

We study the existence of standing waves for a class of nonlinear Schrödinger equations in ℝn, 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. © 2002 Elsevier Science (USA). All rights reserved.
Articolo in rivista - Articolo scientifico
Nonlinear Schrodinger equations
English
2002
108
130
Cingolani, S., Secchi, S. (2002). Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 275(1), 108-130 [10.1016/S0022-247X(02)00278-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/9474
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