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.
Citazione: | Cingolani, S., & Secchi, S. (2002). Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 275(1), 108-130. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields |
Autori: | Cingolani, S; Secchi, S |
Autori: | |
Data di pubblicazione: | 2002 |
Lingua: | English |
Rivista: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/S0022-247X(02)00278-0 |
Appare nelle tipologie: | 01 - Articolo su rivista |