In this paper we study the existence of a positive solution for a nonlinear Dirichlet problem driven by the p-Laplacian and a reaction which has the competing effects of a singular term and of a convection (gradient dependent) term. Using the “frozen” variable method and eventually the Leray-Schauder Alternative Theorem, we show that the problem has a positive smooth solution. We mention that on the gradient dependent perturbation $x\mapsto f(z,x,y)$, we do not impose any bilateral growth condition.

中文翻译：

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对流非线性奇异问题

在本文中，我们研究了由p-拉普拉斯算子和具有奇异项和对流（梯度相关）项的竞争效应的反应驱动的非线性狄利克雷问题的正解的存在。使用“冻结”变量方法和最终的 Leray-Schauder 替代定理，我们表明该问题具有正平滑解。我们提到关于梯度相关的扰动$X\mapsto F(z,X,是)$，我们不强加任何双边增长条件。