Superconductivity in two-band systems with a small concentration of carriers

We consider a superconducter with two features characteristic for high temperature materials: small concentration of charge carriers and overlaping of energy strips on Fermy surface. For $T=0$ in the meanfield approximation the order parameters $\Delta_n$ and chemical potential $\mu$ for bose-condensation of local pairs ($\mu<0$) are found. An equation for the energy $\varepsilon_b$ of the bound state as well as an equality $\varepsilon_b=2\mu$ are obtained. Applying the path integral method to two-zone model the transition from Fermy to Bose exitations in the presence of a two-particle bound state is described. An expression of the Bose condensation temperature and the contribution of a residual Bose interaction between the systems of different dimensions are found.