Special Session 21: Variational, topological, and set-valued methods for differential problems
Contents
The aim of this paper is to prove the existence of a positive solution for a quasi-linear elliptic problem involving the $(p,q)$-Laplacian and a convection term, which means an expression which is not in the principal part and depends on the solution and its gradient. The solution is constructed through an approximating process based on gradient bounds and regularity up to the boundary. The positivity of the solution is shown by applying a new comparison principle which is established here.