  The structure factor for a Bose system with Bose-Einstein condensate is
considered in the frame of the self-consistent mean-field approximation. The
accomplished analysis demonstrates the principal importance of the following
three points: the necessity of preserving the approximation order, the
necessity of taking into account anomalous averages, and the necessity of gauge
symmetry breaking. If any one of these necessary conditions is not satisfied,
calculations yield the appearance of unphysical divergences of the structure
factor, which implies the occurrence of fictitious instability, which
contradicts experiments.
