We consider a nonlinear parametric Neumann problem driven by the anisotropic (p, q)-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter λ varies. We also show the existence of minimal positive solutions \(u_{\lambda }^{*}\) and determine the monotonicity and continuity properties of the map \(\lambda \mapsto u_{\lambda }^{*}\).

我们考虑由各向异性（p，q）-Laplacian驱动的非线性参数Neumann问题以及一个反应，该反应表现出奇异项和参数超线性摄动的组合效应。我们正在寻找积极的解决方案。通过结合使用拓扑和变分工具以及适当的截断和比较技术，我们证明了分叉型结果，描述了随着正参数λ的变化而引起的一组正解。我们还显示了极小正解\（u _ {\ lambda} ^ {*} \）的存在，并确定了图\（\ lambda \ mapsto u _ {\ lambda} ^ {*} \）的单调性和连续性。