In this work we consider the magnetic NLS equation (ℏ/i∇ - A (x))2 u+V (x)u -f (|u|2)u = o in ℝN where N ≥ 3, A: ℝN → ℝ is a magnetic potential, possibly unbounded, V:ℝN → 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:ℝN → C to (0.1), under conditions on the nonlinearity which are nearly optimal. © EDP Sciences, SMAI 2009.
Cingolani, S., Jeanjean, L., Secchi, S. (2009). Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions. ESAIM. COCV, 15(3), 653-675 [10.1051/cocv:2008055].
Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
SECCHI, SIMONE
2009
Abstract
In this work we consider the magnetic NLS equation (ℏ/i∇ - A (x))2 u+V (x)u -f (|u|2)u = o in ℝN where N ≥ 3, A: ℝN → ℝ is a magnetic potential, possibly unbounded, V:ℝN → 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:ℝN → C to (0.1), under conditions on the nonlinearity which are nearly optimal. © EDP Sciences, SMAI 2009.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
