We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian with \(1<q<p\). The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive solutions and prove a bifurcation-type theorem describing in a precise way the set of positive solutions as the parameter varies. Moreover, we show the existence of a minimal positive solution and we study it as a function of the parameter.

中文翻译：

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（p，q）-具有奇异和凹凸非线性的方程

我们考虑由（p，  q）-Laplacian驱动\（1 <q <p \）的非线性Dirichlet问题。该反应是参数性的，并且表现出奇异项以及凹凸非线性的竞争效应。我们正在寻找正解，并证明分叉型定理以精确的方式描述随着参数变化的正解集。此外，我们显示了最小正解的存在，并将其作为参数的函数进行研究。