Elliptic systems with nonlinear diffusion and a convection term

In this paper we prove existence (and summability properties) of solutions for the following elliptic system$ \{ {array}{cl} -{div}(A(x)\,{∇} u) + u^{{λ}} = -{div}( u^{{λ}} \, M(x)\,{∇}ψ) + f(x)\,, & {in }\; Ω , \\ -{div}(M(x)\,{∇}ψ) = uρ\,, & {in }\; Ω , \\ u = 0 = ψ & \;{on}\; ∂Ω , {array} . $under some assumptions on $ {λ} > 0 $, $ ρ > 0 $ and $ f(x) $ in $ L^{{m}}(Ω) $, $ m ≥ 1 $. 'Return of the Patriarca' (see [3])