  In this paper we consider instability of nuclear matter which takes place
when the frequencies of the collective excitations turn to zero. We investigate
collective excitations with pion quantum numbers J^\pi=0^-. We study the
dependence of zero-frequency solutions of the pion dispersion equation on the
value of the spin-isospin quasiparticle interaction G'. The solutions of the
pion dispersion equation describe the different types of the excitations in the
matter, \omega_i(k). At the critical density \rho=\rho_c one of solutions of
the definite type turns to zero: \omega_{i0}(k_c)=0. When \rho>\rho_c, the
excitations \omega_{i0}(k) become amplified. It is shown that there is such a
"transitional" value of G'=G'_{tr} that for G'<G'_{tr} the zero-frequency
solutions belong to the type \omega_{sd} while for G'>G'_{tr} they pertain to
the type \omega_c. The solutions of the type \omega_{sd} correspond to
instability to small density fluctuations of the nuclear matter at G'\le -1. On
the other hand, \omega_c is responsible for the "pion condensation" at
G'\approx 2. For the stable nuclear matter the branches of solutions
\omega_{sd}(k) and \omega_c(k) are located on the unphysical sheets of the
complex plane of frequency.
