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

Silvia CingolaniLouis JeanjeanSimone Secchi — 2009

ESAIM: Control, Optimisation and Calculus of Variations

In this work we consider the magnetic NLS equation ( i - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in N ( 0 . 1 ) where N 3 , 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.

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

Silvia CingolaniLouis JeanjeanSimone Secchi — 2008

ESAIM: Control, Optimisation and Calculus of Variations

In this work we consider the magnetic NLS equation ( i - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in N ( 0 . 1 ) where N 3 , A : N N is a magnetic potential, possibly unbounded, V : N is a multi-well electric potential, which can vanish somewhere, 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.

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