In this paper, we consider a Dirichlet problem driven by an anisotropic (p, q)-differential operator and a parametric reaction having the competing effects of a singular term and of a superlinear perturbation. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter moves. Moreover, we prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

中文翻译：

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奇异各向异性 (p, q)-方程的正解

在本文中，我们考虑由各向异性 ( p ,  q ) 微分算子和具有奇异项和超线性扰动的竞争效应的参数反应驱动的狄利克雷问题。我们证明了一个分岔型定理，描述了参数移动时正解集的变化。此外，我们证明了最小正解的存在，并确定了最小解图的单调性和连续性。