Existence in the nonlinear Schrödinger equation with bounded magnetic field

The paper studies existence of ground states for the nonlinear Schrödinger equation 0.1 $$\begin{aligned} -(\nabla + {\mathbf {i}}A(x))^2u+V(x)u=|u|^{p-1}u ,\quad 2<p<2^*, \end{aligned}$$ with a general external magnetic field. In particular, no lattice periodicity or symmetry field, presence electric field is required.