Existence results for nonlinear elliptic problems with unbounded coefficients

We prove a priori estimates and existence results for Dirichlet problems whose model case is: {−div(|Du|p−2Du(1−|u|)α)=f in Ω,u=0 on ∂Ω, where ΩΩ is a bounded open set in RnRn, n≥2n≥2, 10α>0.