  We discuss some examples of equations of the three-body problem with the
oscillating asymptotics at large momentum: (i) the fixed-center approximation,
(ii) the unitarized equation in the fixed-center approximation, (iii)
Skornyakov--Ter-Martirosyan equation, and (iv) equations with operators used in
the effective field theory, i.e., which can be expanded in power-series with
positive powers of momentum. We show that in the aforementioned three-body
problems the situation analogous to the falling down to the center in the
two-body problem takes place -- there appears an infinite number of bound
states. The energy of these states is not bounded from below. In that sense the
situation is close to the falling down to the center in the two-body problem.
