For the subcritical fractional NLS with harmonic potential, ground states exist, are radial and decreasing, and are orbitally stable if the Cauchy problem is well posed.
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On a Fractional Schr\"odinger equation in the presence of Harmonic potential
For the subcritical fractional NLS with harmonic potential, ground states exist, are radial and decreasing, and are orbitally stable if the Cauchy problem is well posed.