Stability for the time-dependent Hartree equation with positive energy

In this paper, we show that the H1H1 solutions to the time-dependent Hartree equationi∂u∂t=12Δu+2|x|u−(|u|2∗1|x|)uon R3 are stable under the perturbation of parameters. We show that any sequence of H1H1 solutions to the Hartree equations with perturbed parameters admits a weakly convergent subsequence, the weak limit of which is also an H1H1 solution to the Hartree equation. To prove our stability result, we need to deal with the terms involving the potential 1/|x|1/|x| and new estimates will be employed.