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 RN 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. © 2020 Elsevier Ltd