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

Silvia Cingolani; Louis Jeanjean; Simone Secchi

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- 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 (2009): 653-675. <http://eudml.org/doc/244886>.

@article{Cingolani2009,

abstract = {In this work we consider the magnetic NLS equation\[\hspace*\{54.06023pt\}( \frac\{\hbar \}\{i\} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u \, = 0 \, \qquad \mbox\{ in \} \mathbb \{R\}^N\qquad \qquad (0.1)\]where $N \ge 3$, $A \colon \mathbb \{R\}^N \rightarrow \mathbb \{R\}^N$ is a magnetic potential, possibly unbounded, $V \colon \mathbb \{R\}^N \rightarrow \mathbb \{R\}$ 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 $u\colon \mathbb \{R\}^N \rightarrow \mathbb \{C\}$ 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},

language = {eng},

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/244886},

volume = {15},

year = {2009},

}

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

PY - 2009

PB - EDP-Sciences

VL - 15

IS - 3

SP - 653

EP - 675

AB - In this work we consider the magnetic NLS equation\[\hspace*{54.06023pt}( \frac{\hbar }{i} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u \, = 0 \, \qquad \mbox{ in } \mathbb {R}^N\qquad \qquad (0.1)\]where $N \ge 3$, $A \colon \mathbb {R}^N \rightarrow \mathbb {R}^N$ is a magnetic potential, possibly unbounded, $V \colon \mathbb {R}^N \rightarrow \mathbb {R}$ 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 $u\colon \mathbb {R}^N \rightarrow \mathbb {C}$ to (0.1), under conditions on the nonlinearity which are nearly optimal.

LA - eng

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

UR - http://eudml.org/doc/244886

ER -

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