Stability of standing waves for $L^2$-critical nonlinear Schrödinger equations with attractive inverse-power potential

We consider stability of standing waves for L²-critical nonlinear Schrödinger equations with an attractive inverse-power potential. We prove that if the frequency of ground-state standing wave is sufficiently large, then it is orbitally stable. Our results are extensions of the results of Fukuizumi (2005), in which similar results were proven for L²-critical nonlinear Schrödinger equations with smooth potentials such as harmonic potential