  In the present paper, we analyze the properties of the unbalanced
superconducting state on a square lattice with the constant value of the
electron-phonon coupling function. We conduct our analysis in the framework of
the Eliashberg formalism, explicitly considering {\bf k}-dependence of the
electron and phonon dispersion relations. It is found that the balanced
superconducting state does not induce itself in the system due to the high
value of the electron effective mass. However, in the unbalanced case the
thermodynamic properties of the superconducting condensate can be distinctly
different from the predictions of the Bardeen-Cooper-Schieffer theory; when the
coupling constant value in the diagonal channel of the self-energy is
diminished comparing to the non-diagonal channel. This is due to the reduced
dimensionality of the tested system and the strong-coupling effects included in
the Eliashberg formalism.
