For a mass-subcritical fractional Hartree equation with a confining unbounded potential, the ground state set exists and, assuming global well-posedness, the standing waves are orbitally stable.
Cheng, Bound state for the fractional Schr¨ odinger equ ation with unbounded potential
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Orbital Stability of Standing Waves for Fractional Hartree Equation with Unbounded Potentials
For a mass-subcritical fractional Hartree equation with a confining unbounded potential, the ground state set exists and, assuming global well-posedness, the standing waves are orbitally stable.