On radial solutions of semi-relativistic Hartree equations

We consider the semi-relativistic Hartree type equation with nonlocal nonlinearity F(u) = λ(|x| ^-λ * |u| ²)u,0 < γ < n,n ≥ 1. In [2, 3], the global well-posedness (GWP) was shown for the value of γ ∈ (0, 2n/n+1),n ≥ 2 with large data and γ ∈ (2, n), n ≥ 3 with small data. In this paper" we extend the previous GWP result to the case for γ ∈ (1, 2n-1/n),n ≥ 2 with radially symmetric large data. Solutions in a weighted Sobolev space are also studied.