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The theory of thermodynamic properties of two-band superconductor withreduced density charge carriers is developed on the base of phononsuperconducting mechanism with strong electron-phonon interaction. This theoryis adapted to describe the behavior of critical temperature Tc, energy gapsDelta1, Delta2, and the relative jump of electron specific heat (Cs - Cn)/Cn inthe point T = Tc along with the variation of charge carrier density in thecompound MgB2 when substitutional impurities with different valence areintroduced into the system. It is shown, that according to the fillingmechanism of energy bands which overlap on Fermi surface, the quantities Tc,Delta1, Delta2 decrease when this compound is doped with electrons and remainconstant or weakly change when the system is doped with holes. The theoryqualitatively agrees with the experimental data. Also is shown that theconsideration of inter- and intraband scattering of electrons on impuritypotential improves this agreement.Comment: 19 pages, 6 figures, 1 table. to be published in JETP (first number  2007

Superconductivity in two-band systems with a variable carrier density: The case of MgB2