We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian plus an indefinite potential. In the reaction, we have the competing effects of a parametric singular term and of a superlinear perturbation. We examine the nonexistence, existence and multiplicity of positive solutions as the parameter $\lambda >0$ varies.

中文翻译：

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具有不定势和超线性扰动的非线性奇异问题

我们考虑由p拉普拉斯算子加上不定势驱动的参数非线性狄利克雷问题。在反应中，我们有参数奇异项和超线性扰动的竞争效应。我们检查正解的不存在、存在和多重性作为参数$\lambda >0$ 各不相同。