  Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a
local scalar interaction is investigated for various values and momentum
dependence of the scalar Landau parameter $f_0$ in the particle-hole channel.
For $f_0 >0$ the conditions are found when the phase velocity on the spectrum
of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$
there are only damped excitations, and for $f_0<-1$ the spectrum becomes
unstable against a growth of scalar-mode excitations. An effective Lagrangian
for the scalar excitation modes is derived after performing a bosonization
procedure. We demonstrate that the instability may be tamed by the formation of
a static Bose condensate of the scalar modes. The condensation may occur in a
homogeneous or inhomogeneous state relying on the momentum dependence of the
scalar Landau parameter. We show that in the isospin-symmetric nuclear matter
there may appear a metastable state at a subsaturation nuclear density owing to
the condensate. Then we consider a possibility of the condensation of the
zero-sound-like excitations in a state with a non-zero momentum in Fermi
liquids moving with overcritical velocities, provided an appropriate momentum
dependence of the Landau parameter $f_0 (k)>0$. We also argue that in
peripheral heavy-ion collisions the Pomeranchuk instability may occur already
for $f_0 >-1$.
