We consider a nonlinear Robin problem driven by the sum of $p$-Laplacian and $q$-Laplacian (i.e. the $(p,q)$-equation). In the reaction there are competing effects of a singular term and a parametric perturbation $\lambda f(z,x)$, which is Carathéodory and $(p-1)$-superlinear at $x\in \mathbb{R},$ without satisfying the Ambrosetti–Rabinowitz condition. Using variational tools, together with truncation and comparison techniques, we prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $\lambda >0$ varies.

中文翻译：

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具有奇异和超线性项的Robin双相问题

我们考虑由 $p$-拉普拉斯和 $q$-拉普拉斯（即 $（p，q）$-方程）。在反应中，存在奇异项和参数扰动的竞争效应$\lambda F（ž，X）$，这是Carathéodory和 $（p-\mathrm{1个}）$-超线性 $X\in \mathbb{[R}，$不满足Ambrosetti–Rabinowitz条件。使用变分工具，结合截断和比较技术，我们证明了分叉型结果，该结果描述了一组正解的变化作为参数$\lambda >0$ 不同。