  We prove rigorously the occurrence of zero-mode Bose-Einstein condensation
for a class of continuous homogeneous systems of boson particles with
superstable interactions. This is the first example of a translation invariant
continuous Bose-system, where the existence of the Bose-Einstein condensation
is proved rigorously for the case of non-trivial two-body particle
interactions, provided there is a large enough one-particle excitations
spectral gap. The idea of proof consists of comparing the system with specially
tuned soluble models.
