  We study excitations in a normal Fermi liquid with a local scalar
interaction. Spectrum of bosonic scalar-mode excitations 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 (a
Pomeranchuk instability). An effective Lagrangian for the scalar excitation
modes is derived after performing a bosonization procedure. We demonstrate that
the Pomeranchuk 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. 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 $f_0(k)>0$.
