  Using the strong coupling diagram technique, we study the one-band repulsive
Hubbard model on a two-dimensional square lattice in a wide range of chemical
potentials $\mu$. Infinite sequences of diagrams describing interactions of
electrons with spin and charge fluctuations are taken into account. At low
temperatures, regions of the negative electron compressibility are found for
$\mu<0$ and $\mu>U$, where $U$ is the Hubbard repulsion. For even lower
temperatures, in the neighborhood of these regions, states with the phase
separation are revealed.
