  We analyze stability of a fermion system with model repulsive pair
interaction potential. The possibility for different types of restructuring of
the Fermi ground state (at sufficiently great coupling constant) is related to
the analytic properties of such potential. In particular, for the screened
Coulomb law it is shown that the restructuring cannot be of the Fermi
condensation type, known earlier for some exactly solvable models, and instead
it belongs to the class of topological transitions (TT). For this model, a
phase diagram has been built in the variables "screening parameter - coupling
constant" which displays two kinds of TT: a 5/2-kind similar to the known
Lifshitz transitions in metals, and a 2-kind characteristic for a uniform
strongly interacting system.
