Existence results for elliptic problems with gradient terms via a priori estimates

We prove existence of nonnegative solutions of a Dirichlet problem on a bounded smooth domain of R^N for a p-Laplacian elliptic equation with a convection term. Our proof is based on a priori bounds for a suitable a weighted norm involving the distance function form the boundary, obtained by adapting the technique developed by Barrios et al. in 2018 for nonlocal elliptic problems, which is a modification of the classical scaling blow up method due to Gidas and Spruck in the celebrated paper in 1981. The conclusion then follows by using topological degree.