We consider a nonlinear elliptic Dirichlet problem driven by the anisotropic (p, q)-Laplacian and with a reaction which is nonparametric and has the combined effects of a singular and of a superlinear terms. Using variational tools together with truncation and comparison techniques, we show that the problem has at least two positive smooth solutions.

中文翻译：

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各向异性奇异$$ \ varvec {（p，q）} $$（p，q）-方程的正解

我们考虑由各向异性（p，  q）-Laplacian驱动的非线性椭圆Dirichlet问题，其反应是非参数的，并且具有奇异项和超线性项的组合效应。使用变分工具以及截断和比较技术，我们证明该问题至少具有两个肯定的光滑解。