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

Here, the anisotropic <tex-math id="M2">{document}$ (p, q) ${document}</tex-math>-Laplacian <tex-math id="FE1"> {document}$ - ∑i = 1^N∂/∂ x_i( |∂ u/∂ x_i|p_i-2∂ u/∂ x_i) - ∑i = 1^N∂/∂ x_i( |∂ u/∂ x_i|q_i-2∂ u/∂ x_i) = λ uγ-1 document </tex-math> is considered, where <tex-math id="M3">document Ω document</tex-math> is a bounded and regular domain of <tex-math id="M4">document R^N document</tex-math>, <tex-math id="M5">document q_i≤ p_i document</tex-math> for <tex-math id="M6">document i = 1, ⋯, N document</tex-math> and <tex-math id="M7">document γ > 1 ${document}</tex-math>. The existence of positive solution is proved via sub-supersolution method.