Non-radial solutions for the quasi-linear Hénon type $N$-Laplacian Liouville equation

In this paper, we investigate the following quasi-linear weighted $N$-Laplacian Liouville equation \begin{equation*}\label{0} -Δ_N u=|x|^{Nα}e^{u}, \qquad x\in \R^N, \end{equation*} where $N \geq 2$. For $\al>0$, by carefully studying the linearized problem and applying the approximation method and