A positive solution for an anisotropic $ (p,q) $-Laplacian

Here, the anisotropic \begin{document}$ (p, q) $\end{document}-Laplacian style='text-indent:20px;'> \begin{document}$ - \sum\limits_{i = 1}^N\frac{\partial}{\partial x_i}\left( \left|\frac{\partial u}{\partial x_i}\right|^{p_i-2}\frac{\partial x_i}\right) x_i}\right|^{q_i-2}\frac{\partial \lambda u^{\gamma-1} $\end{document} style='text-indent:20px;'>is considered, where id="M3">\begin{document}$ \Omega $\end{document} is a bounded and regular domain of id="M4">\begin{document}$ \mathbb{R}^N $\end{document}, id="M5">\begin{document}$ q_i\leq p_i for id="M6">\begin{document}$ i 1, \cdots, N id="M7">\begin{document}$ \gamma > 1 $\end{document}. The existence positive solution proved via sub-supersolution method.