The aim of the current paper is to illustrate, in a simple example, our
recent, very general, rigorous results
on the dynamical properties of fermions and quantum-spin systems with
long-range, or mean-field, interactions, in infinite volume. We consider
here the strong-coupling BCS-Hubbard model, because this example is very pedagogical and,
at the same time, physically relevant for it highlights the impact of the
(screened) Coulomb repulsion on ($s$-wave) superconductivity.