Stability of $n$-particle pseudorelativistic systems

For a system $Z_n$ of $n$ identical pseudorelativistic particles, we show that under some restrictions on the pair interaction potentials, there is an infinite sequence of numbers $n_s$, $s=1,2,\dots$, such that the system $Z_n$ is stable for $n=n_s$, and the inequality $\sup_sn_{s+1}n_s^{-1}<+\infty$ holds. Furthermore, we show that if the system $Z_n$ is stable, then the discrete spectrum of the energy operator for the relative motion of the system $Z_n$ is nonempty for some values of the total momentum of the particles in the system. The stability of $n$-particle systems was previously studied only for nonrelativistic particles.