We study the quasilinear elliptic equation
$ \begin{equation*} -Qu = e^u ~~~~\mbox{in}~~~~ \Omega\subset \mathbb{R}^{N}, \end{equation*} $
where the operator
$ Qu: = \sum\limits_{i = 1}^{N}\frac{\partial}{\partial x_{i}}(F(\nabla u)F_{\xi_{i}}(\nabla u)). $
Here
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