n 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.

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions / Cingolani, Silvia; Jeanjean, L; Secchi, S.. - In: ESAIM. COCV. - ISSN 1292-8119. - 15:3(2009), pp. 653-675. [10.1051/cocv:2008055]

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

CINGOLANI, Silvia;
2009-01-01

Abstract

n 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.
2009
Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions / Cingolani, Silvia; Jeanjean, L; Secchi, S.. - In: ESAIM. COCV. - ISSN 1292-8119. - 15:3(2009), pp. 653-675. [10.1051/cocv:2008055]
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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/9604
Citazioni
  • Scopus 52
  • ???jsp.display-item.citation.isi??? 49
social impact