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We investigate the density instabilities present in the infinite-UHubbard-Holstein model both at zero and finite momenta as well as theoccurrence of Cooper instabilities with a specific emphasis on the role oflong-range Coulomb forces. In carrying out this analysis a special attention isdevoted to the effects of the strong local $e$-$e$ interaction on the $e$-$ph$coupling and particularly to both the static and dynamic screening processesdressing this coupling. We also clarify under which conditions in stronglycorrelated electron systems a weak additional interaction, e.g. aphonon-mediated attraction, can give rise to a charge instability. In thepresence of long-range Coulomb forces, the frustrated phase separation leads tothe formation of incommensurate charge density waves.  These instabilities, in turn, lead to strong residual scattering processesbetween quasiparticles and to superconductivity, thus providing an interestingclue to the interpretation of the physics of the copper oxides.Comment: 18 pages+13 postscript figure

Charge-density waves and superconductivity as an alternative to phase separation in the infinite-UHubbard-Holstein model