We will focus on the double weighted critical quasilinear Hénon equation \(\begin{aligned} \displaystyle -\hbox {div}\left( |\nabla u|^{p-2}\nabla u\right) =|x|^{\alpha _1}|u|^{p^*(\alpha _1)-2}u - \lambda |x|^{\alpha _2}|u|^{p^*(\alpha _2)-2} u \end{aligned}\) with the parameter \(\lambda >0\) in the whole space \({\mathbb {R}^N}\) , the half space \({\mathbb {R}^N_+}\) , an open cone or a bounded domain \(\Omega \) . On one hand, we will prove that the equation has only trivial solution when \(\lambda >\lambda ^*\) , a positive number having explicit expression. On the other hand, we will prove that the equation has a nontrivial solution for \(\lambda >0\) small. Finally, we will establish the asymptotic behavior of solutions of equation as \(\lambda \rightarrow 0^+\) .
