Quasilinear elliptic systems with measure data

We study the existence of solutions of quasilinear elliptic systems involving N equations and a measure on the right hand side, with the form −∑i=1nuβ)=μα in Ω,u=0 on ∂Ω, where α∈1,…,N is the equation index, Ω is an open bounded subset of Rn, u:Ω→RN and μ is a finite Randon measure on Rn with values in RN. Existence of a solution is proved for two different sets of assumptions on A. Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter.