Ground states for the pseudo-relativistic Hartree equation with external potential

We prove the existence of positive ground state solutions to the pseudo-relativistic Schrodinger equation root-Delta vertical bar m(2)u vertical bar Vu = (W * vertical bar u vertical bar(theta))vertical bar u vertical bar(theta-2) u in R-N, u is an element of H-1/2(R-N), where N >= 3, m > 0, V is a bounded external scalar potential and W is a radially symmetric convolution potential satisfying suitable assumptions. We also provide some asymptotic decay estimates of the found solutions.