We prove existence of nonnegative solutions of a Dirichlet problem on a bounded smooth domain of ${\mathbb{R}}^N$ for a $p$-Laplacian elliptic equation with a convection term. Our proof is based on a priori bounds for a suitable weighted norm involving the distance function from the boundary, obtained by adapting the technique developed by Barrios et al. [4] for nonlocal elliptic problems, which is a modification of the classical scaling blow up method due to Gidas and Spruck in the celebrated paper [25]. The conclusion then follows by using topological degree.

中文翻译：

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具有先验估计的带有梯度项的椭圆问题的存在结果

我们证明在Dirichlet问题的有界光滑域上非负解的存在 ${\mathbb{[R}}^{ñ}$ 为一个 $p$-具有对流项的拉普拉斯椭圆方程。我们的证明是基于适合优先权范围的先验范围，该加权范围涉及到边界的距离函数，这是通过改编Barrios等人开发的技术获得的。[4]针对非局部椭圆问题，这是著名论文[25]中Gidas和Spruck提出的经典比例缩放方法的改进。然后通过使用拓扑度得出结论。