Ground states for semi-relativistic Schrödinger-Poisson-Slater energies

Jacopo Bellazzini, Tohru Ozawa, Nicola Visciglia

We prove the existence of ground states for the semi-relativistic Schrödinger-Poisson-Slater energy $$I^{α,β}(ρ)=\inf_{\substack{u\in H^\frac 12(\R^3) \int_{\R^3}|u|^2 dx=ρ}} \frac…