The aim of this paper is to classify the solutions of the critical nonlocal
equation with weighted nonlocal term $$-\Delta u
=\frac{1}{|x|^{\alpha}}\left(\int_{\mathbb{R}^{N}}\frac{|u(y)|^{2_{\alpha,\mu}^{\ast}}}
{|x-y|^{\mu}|y|^{\alpha}}dy\right)|u|^{2_{\alpha,\mu}^{\ast}-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm}
\mathbb{R}^{N} $$ and the subcritical case of the form $$-\Delta u+u
=\frac{1}{|x|^{\alpha}}\left(\int_{\mathbb{R}^{N}}\frac{|u(y)|^{p}}
{|x-y|^{\mu}|y|^{\alpha}}dy\right)|u|^{p-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm}
\mathbb{R}^{N}. $$ where $N\geq3$, $0<\mu