On nonlinear elliptic equations with singular lower order term

We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like − div ( (a(x) + |u|)∇u ) = f |u|γ in Ω, u = 0 on ∂Ω, where Ω is a bounded open subset of RN(N ≥ 2), a(x) is a measurable nonnegative function, q, γ > 0 and the source f is a nonnegative (not identicaly zero) function belonging to Lm(Ω) for some m ≥ 1. Our results will depend on the summability of f and on the values of q, γ > 0.