Displaying similar documents to “The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.”

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

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this work we consider the magnetic NLS equation ( ℏ i ∇ - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in ℝ N ( 0 . 1 ) where N ≥ 3 , A : ℝ N → ℝ N is a magnetic potential, possibly unbounded, V : ℝ N → 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 : ℝ N → ℂ to (0.1), under conditions on the nonlinearity which are nearly optimal.