Proof of Bose-Einstein Condensation for Interacting Gases with a   One-Particle Spectral Gap
  Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems. 
J. Lauwers, A. Verbeure, V. A. Zagrebnov