  We study the emergence of Faraday waves in cigar-shaped collisionally
inhomogeneous Bose-Einstein condensates subject to periodic modulation of the
radial confinement. Considering a Gaussian-shaped radially inhomogeneous
scattering length, we show through extensive numerical simulations and detailed
variational treatment that the spatial period of the emerging Faraday waves
increases as the inhomogeneity of the scattering length gets weaker, and that
it saturates once the width of the radial inhomogeneity reaches the radial
width of the condensate. In the regime of strongly inhomogeneous scattering
lengths, the radial profile of the condensate is akin to that of a hollow
cylinder, while in the weakly inhomogeneous case the condensate is cigar-shaped
and has a Thomas-Fermi radial density profile. Finally, we show that when the
frequency of the modulation is close to the radial frequency of the trap, the
condensate exhibits resonant waves which are accompanied by a clear excitation
of collective modes, while for frequencies close to twice that of the radial
frequency of the trap, the observed Faraday waves set in forcefully and quickly
destabilize condensates with weakly inhomogeneous two-body interactions.
