We analyzed a self-similar solution during the core collapse of a massive star with energy losses by neutrino radiation. Two mechanisms of neutrino emission are considered: Urca process and pair neutrino emission. It is shown there are no conditions where collapse of a very massive star may stay stable, while for less massive star it is possible. Using obtained relations we found characteristic features of developing of the instability, thereby showing that it may lead to nonuniform supernovae explosion.
$^1$Keldysh Institute of Applied Mathematics RAS\
$^2$Laboratoire d'Annecy-le-Vieux de Physique Theorique
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