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

Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields / Cingolani, Silvia; Secchi, S.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 275:1(2002), pp. 108-130. [10.1016/S0022-247X(02)00278-0]

Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields

CINGOLANI, Silvia;
2002-01-01

Abstract

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
2002
Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields / Cingolani, Silvia; Secchi, S.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 275:1(2002), pp. 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/11589/11700
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