Ground states for pseudo-relativistic Hartree equations of critical type

We study the existence of ground state solutions for a class of non-linear pseudo-relativistic Schr"odinger equations with critical two-body interactions. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such a problem using variational methods after transforming the problem to an elliptic equation with a nonlinear Neumann boundary conditions.