On Hartree type problems with mass subcritical perturbations

We investigate the normalized solutions of the Hartree type equation with the external harmonic potential and the mass subcritical perturbation term, which can be characterized by the constraint minimization problem. Using direct energy estimates and regularity analysis, we establish the concentration phenomenon of positive minimizers. Based on this, the local uniqueness of positive minimizers is also proved by overcoming certain decay properties of the associated solution sequences and the variability of the harmonic potential under translations.