Existence of ground states for nonlinear, pseudo-relativistic Schrodinger equations

We study existence and regularity of positive stationary solutions for a class of nonlinear pseudo-relativistic Schrodinger equations. Such equations are characterized by a nonlocal pseudo-differential operator closely related to the square-root of the Laplacian. We investigate such problems using critical point theory after transforming them to elliptic equations with nonlinear Neumann boundary conditions.