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We study the stationary states of the semi-relativistic Schr\"odinger-Poissonsystem in the repulsive (plasma physics) Coulomb case. In particular, weestablish the existence and the nonlinear stability of a wide class ofstationary states by means of the energy-Casimir method. We generalize theglobal well-posedness result of our previous work for the semi-relativisticSchr\"odinger-Poisson system to spaces with higher regularity.

Existence and nonlinear stability of stationary states for the semi-relativistic Schr\"odinger-Poisson system