The Hamiltonian of the electron-phonon interaction with polar optical
vibrations in multilayer structures is used to derive a Hamiltonian th
at describes, through the introduction of unitary transformations of B
ogolyubov type, the formation of pairs of electrons with opposite spin
s and 2D wave vectors. The distribution function for the considered sy
stems is derived using Zubarev's nonequilibrium statistical operator m
ethod. An evolution equation is obtained for the distribution function
, and under certain simplifying assumptions an integral equation for t
he superconducting energy gap is obtained. The parameters of rome stru
ctures are used in a numerical investigation of the temperature depend
ence of the gap for different thicknesses of the conducting layer. It
is shown that some of the structures may be candidates for high-temper
ature superconductors.