Remarks about a generalized pseudo-relativistic Hartree equation

With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem

${(?\mathrm{\Delta }+m^2)}^{\sigma }u+Vu=(W?F(u))f(u)\text{in }{\mathbb{R}}^N,$

where $0<\sigma <1$, V is a bounded continuous potential and F the primitive of f. We also show results about the regularity of any solution of this problem.