Existence of solutions for degenerate quasilinear elliptic equations

This paper deals with a class of degenerate quasilinear elliptic equations of the form −div(a(x,u,∇u)=g−div(f)−div(a(x,u,∇u)=g−div(f), where a(x,u,∇u)a(x,u,∇u) is allowed to be degenerate with the unknown uu. We prove existence of bounded solutions under some hypothesis on ff and gg. Moreover we prove that there exists a renormalized solution in the case where g∈L1(Ω)g∈L1(Ω) and f∈(Lp′(Ω))Nf∈(Lp′(Ω))N.