  We study the interplay between few- and many-body physics in Bose gases near
resonance. The effect of condensates on the two-body running coupling constant
is investigated via imposing a boundary condition on a self-consistent
renormalization flow equation. Bose gases are found to become nearly
fermionized when the chemical potential as a function of scattering lengths
reaches a maximum and the atomic condensates lose meta-stability. The maximum
and accompanied insta- bility are illustrated as a precursor of the sign change
of g_2, the renormalized two-body interaction between condensed atoms from
effectively repulsive to effectively attractive when approaching res- onance
even though the scattering length is still positive. This occurs when dimers,
under the influence of condensates, emerge at zero energy in the atomic gases
at a finite positive scattering length.
