Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 653-675.

In this work we consider the magnetic NLS equation

 $\phantom{\rule{54.06023pt}{0ex}}{\left(\frac{\hslash }{i}\nabla -A\left(x\right)\right)}^{2}u+V\left(x\right)u-{f\left(|u|}^{2}\right)u\phantom{\rule{0.166667em}{0ex}}=0\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{4pt}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}{ℝ}^{N}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\left(0.1\right)$
where $N\ge 3$, $A:{ℝ}^{N}\to {ℝ}^{N}$ is a magnetic potential, possibly unbounded, $V:{ℝ}^{N}\to ℝ$ is a multi-well electric potential, which can vanish somewhere, $f$ is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution $u:{ℝ}^{N}\to ℂ$ to (0.1), under conditions on the nonlinearity which are nearly optimal.

DOI : https://doi.org/10.1051/cocv:2008055
Classification : 35J20,  35J60
Mots clés : nonlinear Schrödinger equations, magnetic fields, multi-peaks
@article{COCV_2009__15_3_653_0,
author = {Cingolani, Silvia and Jeanjean, Louis and Secchi, Simone},
title = {Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {653--675},
publisher = {EDP-Sciences},
volume = {15},
number = {3},
year = {2009},
doi = {10.1051/cocv:2008055},
mrnumber = {2542577},
language = {en},
url = {http://www.numdam.org/item/COCV_2009__15_3_653_0/}
}
Cingolani, Silvia; Jeanjean, Louis; Secchi, Simone. Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 653-675. doi : 10.1051/cocv:2008055. http://www.numdam.org/item/COCV_2009__15_3_653_0/

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