Solvability of quasilinear degenerated elliptic equations with L¹ data

In this paper we prove the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x, u, ∇u) = f, where A is a Leray-Lions operator from into its dual, while g(x, s, ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong to L¹(Ω).