# Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani; Louis Jeanjean; Simone Secchi

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 15, Issue: 3, page 653-675
- ISSN: 1292-8119

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topCingolani, Silvia, Jeanjean, Louis, and Secchi, Simone. "Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2008): 653-675. <http://eudml.org/doc/90931>.

@article{Cingolani2008,

abstract = {
In this work we consider the magnetic NLS equation
$$ ( \frac\{\hbar\}\{i\} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u \, = 0 \, \qquad \mbox\{ in \} \mathbb\{R\}^N\qquad\qquad(0.1)$$
where $N \geq 3$, $A \colon \mathbb\{R\}^N \to \mathbb\{R\}^N$ is a magnetic potential,
possibly unbounded, $V \colon \mathbb\{R\}^N \to \mathbb\{R\}$ 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 $u\colon \mathbb\{R\}^N \to \mathbb\{C\}$ to (0.1), under conditions
on the nonlinearity which are nearly optimal.
},

author = {Cingolani, Silvia, Jeanjean, Louis, Secchi, Simone},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Nonlinear Schrödinger equations; magnetic fields;
multi-peaks; nonlinear Schrödinger equations; multi-peaks},

language = {eng},

month = {8},

number = {3},

pages = {653-675},

publisher = {EDP Sciences},

title = {Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions},

url = {http://eudml.org/doc/90931},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Cingolani, Silvia

AU - Jeanjean, Louis

AU - Secchi, Simone

TI - Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/8//

PB - EDP Sciences

VL - 15

IS - 3

SP - 653

EP - 675

AB -
In this work we consider the magnetic NLS equation
$$ ( \frac{\hbar}{i} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u \, = 0 \, \qquad \mbox{ in } \mathbb{R}^N\qquad\qquad(0.1)$$
where $N \geq 3$, $A \colon \mathbb{R}^N \to \mathbb{R}^N$ is a magnetic potential,
possibly unbounded, $V \colon \mathbb{R}^N \to \mathbb{R}$ 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 $u\colon \mathbb{R}^N \to \mathbb{C}$ to (0.1), under conditions
on the nonlinearity which are nearly optimal.

LA - eng

KW - Nonlinear Schrödinger equations; magnetic fields;
multi-peaks; nonlinear Schrödinger equations; multi-peaks

UR - http://eudml.org/doc/90931

ER -

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