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In this paper we study long time dynamics (i.e., scattering and blow-up) ofsolutions for the focusing NLS with a repulsive inverse-power potential andwith initial data lying exactly at the mass-energy threshold, namely, when$E_{V}(u_{0})M(u_{0})=E_{0}(Q)M(Q)$. Moreover, we prove failure of the uniformspace-time bounds at the mass-energy threshold.

Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential