The paper presents original expressions for the temperature of the superconducting transition T_C as well as for the coefficient of the isotope effect α in non-adiabatic superconductors with strong electron correlations and variable charge-carrier density. The equation for the cutoff momentum Q_c due to strong electron correlations is also derived. The dependence of the quantities T_c, α and Q_c on the charge-carrier density n in quasi-two-dimensional and threedimensional systems is studied. At the point of its maximum, T_C is shown to easily reach the values characteristic of high-T_c materials because of non-adiabaticity. The quantity α depends strongly on the theory parameters and achieves values in the range 0.2-0.4. It is found that the field of existence of superconductivity and the behaviour of Q_c (n) are determined by the dimensionality of the system.