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.
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