An existence result for Schrödinger equations with magnetic fields and exponential critical growth

We show the existence of a complex solution to the following magnetic Schrödinger equation -(∇+iA(x))2u+u=f(|u|2)uinR2where A: R2→ R2 is a suitable magnetic potential and f satisfies exponential critical growth assumptions at infinity. We exploit some recent results established by means of a Trudinger-Moser inequality to the corresponding real equation in absence of the magnetic field (i.e., A(x) = 0). © 2017, Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature.