Existence in the nonlinear Schrödinger equation with bounded magnetic field

The paper studies existence of ground states for the nonlinear Schrödinger equation 0.1-(∇+iA(x))2u+V(x)u=|u|p-1u,2<p<2∗,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -(\nabla + {\mathbf {i}}A(x))^2u+V(x)u=|u|^{p-1}u ,\quad 2<p<2^*, \end{aligned}$$\end{document}with a general external magnetic field. In particular, no lattice periodicity or symmetry of the magnetic field, or presence of external electric field is required.