Asymptotic profile of ground states for the Schrödinger–Poisson–Slater equation

We study the Schrödinger–Poisson–Slater equation − Δ u + u + λ ( I 2 ∗ | u | 2 ) u = | u | p − 2 u in R 3 , where p ∈ ( 3 , 6 ) and λ > 0 . By using direct variational analysis based on the comparison of the ground state energy levels, we obtain a characterization of the limit profile of the positive ground states for λ → ∞ .