Fermi-liquid effects in the Hubbard model

Properties of an electronic system with a very strong electron-electron interaction are studied. The equation of state is obtained, and the temperature and concentration dependences of the hydrodynamic sound and magnetic susceptibility are calculated. A low-temperature domain of instability corresponding to phase segregation is found. This domain is located inside the wide region of Cooper instability. The equation for zero-sound oscillations is obtained with regard to the substantial anisotropy of the energy spectrum.