Regularizing effect of absorption terms in singular problems

We prove existence of solutions to problems whose model is {−Δpu+uq=[Formula presented]inΩ,u≥0inΩ,u=0on∂Ω where Ω is an open bounded subset of RN (N≥2), Δpu is the p-laplacian operator for 1≤p0, γ≥0 and f is a nonnegative function in Lm(Ω) for some m≥1. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case γ≤1. We also study uniqueness of these solutions as well as examples which show the optimality of the results. Finally, we find local W1,p-solutions in case γ>1.