We consider a nonlinear Dirichlet problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.

中文翻译：

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对流的奇异双相问题

我们考虑由\（p \）- Laplacian和\（q \）- Laplacian（双相方程）之和驱动的非线性Dirichlet问题。在反应中，我们具有奇异项和局部定义的与梯度相关的项（对流）的组合作用。通过使用变分和拓扑方法的混合以及适当的截断和比较技术，我们证明了正光滑解的存在。