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=1n∂∂xi(∑β=1N∑j=1nai,jα,β(x,u)∂∂xjuβ)=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.