Existence of Positive Eigenfunctions to an Anisotropic Elliptic Operator via Sub-Super Solutions Method

Using the sub-supersolution method we study the existence of positive solutions for the anisotropic problem begin{equation} -sum_{i=1}^Nfrac{partial}{partial x_i}left( left|frac{partial u}{partial x_i}right|^{p_i-2}frac{partial u}{partial x_i}right)=lambda u^{q-1} end{equation} where $Omega$ is a bounded and regular domain of $mathbb{R}^N$, $q>1$ and $lambda>0$.