  We study the Cu-O valence instability (VI) and the related phase separation
(PS) driven by Cu-O nearest-neighbor repulsion $U_{pd}$, using an effective
extended one-band Hubbard model ($H_{eff}$) obtained from the extended
three-bandHubbard model, through an appropriate low-energy reduction. $H_{eff}$
is solved by exact diagonalization of a square cluster with 10 unit cells and
also within a slave-boson mean-field theory. Its parameters depend on doping
for $U_{pd}\neq 0$ or on-site O repulsion $U_p\neq 0$. The results using both
techniques coincide in that there is neither VI nor PS for doping levels
$x<0.5$ if $U_{pd}\lesssim 2$ eV. The PS region begins for $U_{pd}\gtrsim 2$ eV
at large doping $x>0.6$ and increases with increasing $U_{pd}$. The PS also
increases with increasing on-site Cu repulsion $U_d$.
