By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dxdy− (1/p)∫ℝ3|u|pdx:u∈Bρ}can be achieved for p∈(2,3)and ρ>0small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. Moreover, the properties of Iρ2/ρ2and the associated Lagrange multiplier λρare also given if p∈(2,8/3].
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