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

Abstract

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 $N\ge 3$, $A:{\mathbb{R}}^N\to {\mathbb{R}}^N$ is a magnetic potential, possibly unbounded, $V:{\mathbb{R}}^N\to \mathbb{R}$ 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