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

Cingolani, Silvia; Jeanjean, Louis; Secchi, Simone

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

Authors

Cingolani, Silvia

Jeanjean, Louis

Secchi, Simone

Description

In the work we consider the magnetic NLS equation (\frac{\hbar}{i} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u = 0 \quad {in} \R^N where $N \geq 3$, $A \colon \R^N \to \R^N$ is a magnetic potential, possibly unbounded, $V \colon \R^N \to \R$ 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 $u\colon \R^N \to \C$, under conditions on the nonlinearity which are nearly optimal.
Important modification in the last part of the paper