We consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter \(\lambda \). Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

我们考虑由 ( p ,  q )-拉普拉斯算子驱动的参数非线性非齐次狄利克雷问题，其反应涉及奇异项加上不满足 Ambrosetti-Rabinowitz 条件的超线性反应。本文的主要目标是寻找积极的解决方案，我们的方法基于使用变分工具结合适当的截断和比较技术。我们证明了一个分岔型定理，它以精确的方式描述了正解集对参数\(\lambda \)的依赖性。此外，我们产生最小正解并确定最小正解图的单调性和连续性。