On the stability of $N$-particle systems

For a large class of $N$-particle boson and fermion systems we prove the existence of an increasing sequence of numbers $N_p$ such that the $N_p$ – particle system is stable, $p=1,2,\dots$. In addition, for fermions and any allowed symmetry type $\alpha$ sufficient condition is found for the existence of an increasing sequence of numbers $N_s(\alpha)$ such that a system of $N_s(\alpha)$ fermions has a bound state of symmetry $\alpha$.