  Momentum and doping dependence of the static charge susceptibility \chi(q) in
the t-t'-J model is investigated. Correlations lead to a strongly momentum
dependent renormalization of \chi(q). The charge susceptibility near (\pi,\pi)
region of the Brillouin zone is strongly suppressed as the hole density \delta
is decreased. However, contrary to naive expectations, \chi(q) around q =
(\pi,0) and (0,\pi) remains large and practically unchanged at \delta \sim
0.1-0.5. This effect is consistent with a tendency towards low-energy charge
fluctuations with the wave vectors along the \Gamma-X direction, reported in
earlier studies. Our main finding is that the above trends are amplified by
J-driven pairing effects, indicating that the pseudogap formation may promote
the charge inhomogeneity. The next-nearest hopping t' leads to weakening of the
above momentum-selective renormalizations of \chi(q). We analyze the effects of
long-range Coulomb interaction, taking into account a layered structure of
cuprates. As an application, the results are discussed in the context of
bond-stretching phonon softening in hole-doped cuprates. In particular, a
peculiar doping and momentum dependence of the electron-phonon coupling
constant is found.

Strongly Correlated Electrons