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

( i-A(x)) 2 u+V(x)u-f(|u| 2 )u=0in N (0.1)
where N3, A: N N is a magnetic potential, possibly unbounded, V: N 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: N to (0.1), under conditions on the nonlinearity which are nearly optimal.

DOI : 10.1051/cocv:2008055
Classification : 35J20, 35J60
Mots clés : nonlinear Schrödinger equations, magnetic fields, multi-peaks
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     title = {Multi-peak solutions for magnetic {NLS} equations without non-degeneracy conditions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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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://archive.numdam.org/articles/10.1051/cocv:2008055/

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