Stationary Solutions of Nonlinear Schrödinger Equations with an External Magnetic Field

In this paper we study the existence of stationary solutions of some Schrödinger equations with an external magnetic field. We obtain these solutions by solving appropriate minimization problems for the corresponding energy-functional. These problems which are a priori not compact are solved by the use of the so-called concentration-compactness method. We also prove the existence of solutions for the generalized Hartree-Fock equations which model the interaction of electrons and static nucleii through a coulombic potential and under the action of an external magnetic field.