| Issue |
ESAIM: COCV
Volume 15, Number 3, July-September 2009
|
|
|---|---|---|
| Page(s) | 653 - 675 | |
| DOI | https://doi.org/10.1051/cocv:2008055 | |
| Published online | 20 August 2008 | |
Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
1
Dipartimento di Matematica, Politecnico di
Bari, via Orabona 4, 70125 Bari, Italy. s.cingolani@poliba.it
2
Équipe de Mathématiques
(UMR CNRS 6623), 16 Route de Gray, 25030 Besançon, France.
louis.jeanjean@univ-fcomte.fr
3
Dipartimento di Matematica ed Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy. Simone.Secchi@unimib.it
Received:
16
October
2007
Revised:
13
March
2008
In this work we consider the magnetic NLS equation
where 
, 
is a magnetic potential,
possibly unbounded, 
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 
to (0.1), under conditions
on the nonlinearity which are nearly optimal.
Mathematics Subject Classification: 35J20 / 35J60
Key words: Nonlinear Schrödinger equations / magnetic fields / multi-peaks
© EDP Sciences, SMAI, 2008
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