Remarks on positive solutions to a p-Laplacian problem with a possibly singular nonlinearity

In this paper, we combine variational methods and truncation techniques to study the existence of a positive weak solution for a quasilinear elliptic problem driven by the p -Laplacian operator involving a reaction term which might or might not have a singularity at 0. Furthermore, provided that solutions belong to C1(Ω), uniqueness is achieved using a Díaz-Saá type argument, which relies on a Brézis-Oswald assumption on the nonlinearity. Additionally, in the superlinear case, we give a multiplicity result that applies when an Ambrosetti-Rabinowitz type condition is fulfilled, e.g. in the concave-convex context.