  A consistent microscopic theory of superconductivity for strongly correlated
electronic systems is presented. The Dyson equation for the normal and
anomalous Green functions for the projected (Hubbard) electronic operators is
derived. To compare various mechanisms of pairing, the extended Hubbard model
is considered where the intersite Coulomb repulsion and the electron-phonon
interaction are taken into account. We obtain the $d$-wave pairing with
high-$T_c$ induced by the strong kinematical interaction of electrons with spin
fluctuations, while the Coulomb repulsion and the electron-phonon interaction
are suppressed for the $d$-wave pairing. These results support the
spin-fluctuation mechanism of high-temperature superconductivity in cuprates
previously proposed in phenomenological models.
