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.File in questo prodotto:
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