A study is made of superconductivity in systems with a variable density of charge carriers, strong electronic correlations (which influence the electron-phonon interaction), and low Fermi energies. This last circumstance leads to violation of the Migdal theorem and makes it necessary to take into account the vertex and crossed diagrams for the electron-phonon interaction (P_v,P_c). Two- and three-dimensional systems are considered. The values of P_v and P_c are found, and the equation for the momentum cutoff Q_c of the electron-phonon interaction is derived. The dependence of this quantity on the concentration of charge carriers is demonstrated. Expressions are obtained for the superconducting transition temperature T_c and the isotope exponent α, and their behavior as functions of the carrier concentration is analyzed. The values of the carrier densities for which superconductivity can occur in two- and three-dimensional systems are determined.