Uniqueness of solution for logarithm Choquard equation

In this paper, we prove the uniqueness of positive solutions for the following Choquard equation involving logarithm convolution {equation*}-Δ u(x)=e^{[∫R^N ln{|y|/|x-y|}u(y)2N/N-2\,dy]}u(x)N/N-2 { in}\ R^N{equation*} where N≥ 3 . Under the assumptions that {equation*}{∫R^N} e^{{N+2}2[∫R^N ln{|y|/|x-y|}u(y)2N/N-2\,dy]}\,dx < ∞,\ {∫R^N} uN+2/N-2\,dx < ∞ { and } {∫R^N} u2N/N-2\,dx < ∞,{equation*} we show that any positive solution of the above equation must have the following form {equation*}u(x)=(Cε/ε^2+|x-x_0|^2)^{{N-2}2},{equation*} where C is a positive constant, ε > 0 and x₀∈ RN are two parameters.