  We investigate the microscopic mechanism of charge instabilities and the
formation of inhomogeneous states in systems with strong electron correlations.
It is demonstrated that within a strong coupling expansion the single-band
Hubbard model shows an instability towards phase separation and extend the
approach also for an analysis of phase separation in the Hubbard-Kanamori
hamiltonian as a prototypical multiband model. We study the pairing
fluctuations on top of an inhomogeneous stripe state where superconducting
correlations in the extended s-wave and d-wave channels correspond to
(anti)bound states in the two-particle spectra. Whereas extended s-wave
fluctuations are relevant on the scale of the local interaction parameter U, we
find that d-wave fluctuations are pronounced in the energy range of the active
subband which crosses the Fermi level. As a result low energy spin and charge
fluctuations can transfer the d-wave correlations from the bound states to the
low energy quasiparticle bands. Our investigations therefore help to understand
the coexistence of stripe correlations and d-wave superconductivity in
cuprates.
