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.
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Articolo in rivista - Articolo scientifico
Scientifica
Nonlinear Schroedinger equations
English
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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].
Cingolani, S; Jeanjean, L; Secchi, S
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/7610
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