Existence and Asymptotic Behavior of Normalized Ground States for a Weighted Elliptic System with Caffarelli--Kohn--Nirenberg Critical Exponent

In this paper, we study the coupled singular weighted elliptic system $$\left\{ \begin{aligned} -\operatorname{div}(|x|^{-2a}\nabla u)+λ_1 \frac{u}{|x|^{2a}}&=βp\frac{|v|^q|u|^{p-2}u}{|x|^{b(p+q)}}+\frac{|u|^{2^{\sharp}-2}u}{|x|^{b2^{\sharp}}},\quad\text{in}~\mathbb{R}^N, -\operatorname{div}