  The lowest order constrained variational method [Phys. Rev. Lett. {\bf 88},
210403 (2002)] has been generalized for a dilute (in the sense that the range
of interatomic potential is small compared with inter-particle spacing) uniform
gas of bosons near the Feshbach resonance using the multi-channel zero-range
potential model. The method has been applied to Na (F=1, m_F=1) atoms near the
907G Feshbach resonance. It is shown that at high densities there are
significant differences between our results for the real part of energy per
particle and the one-channel zero-range potential approximation. We point out
the possibility of stabilization of the uniform condensate for the case of
negative scattering length.
