  Eliashberg theory (ET) generalized for the account of the peculiar properties
of the finite zone width electron-phonon (EP) systems with the non constant
electron density of states, the electron-hole nonequivalence, chemical
potential renormalization with doping and frequency, and electron correlations
in the vertex function is used for the study of Tc in cuprates. The phonon
contribution to the nodal anomalous electron Green function (GF) in cuprates is
considered. The pairing on the full width of the electron zone was taken into
account, not just on the Fermi surface. It is found that the finite zone width
phenomenon in the newly derived Eliashberg equations for the finite zone width
EP system together with the abrupt fall of the density of states above the
Fermi surface are the crucial factors for the appearance of the high
temperature superconductivity phenomenon. It is shown that near the optimal
doping in the hole-doped cuprates high value is reproduced with the EP
interaction constant obtained from tunnel experiments.
