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

Abstract

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

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