Existence and concentration results for some fractional Schr\"odinger equations in $\mathbb{R}^{N}$ with magnetic fields

Abstract

We consider some nonlinear fractional Schr\"odinger equations with magnetic field and involving continuous nonlinearities having subcritical, critical or supercritical growth. Under a local condition on the potential, we use minimax methods to investigate the existence and concentration of nontrivial weak solutions.