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Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 3 / July 2009
- Published online by Cambridge University Press:
- 20 August 2008, pp. 653-675
- Print publication:
- July 2009
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- Article
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In this work we consider the magnetic NLS equation $$ ( \frac{\hbar}{i} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u \, = 0 \, \qquad \mbox{ in } \mathbb{R}^N\qquad\qquad(0.1)$$
where $N \geq 3$ 
, $A \colon \mathbb{R}^N \to \mathbb{R}^N$ 
is a magnetic potential,possibly unbounded, $V \colon \mathbb{R}^N \to \mathbb{R}$ 
is a multi-well electricpotential, which can vanish somewhere, f is a subcriticalnonlinear term. We prove the existence of a semiclassical multi-peaksolution $u\colon \mathbb{R}^N \to \mathbb{C}$ 
to (0.1), under conditionson the nonlinearity which are nearly optimal.
