Existence of solutions for some nonlinear elliptic unilateral problems with measure data

In this paper, we prove the existence of an entropy solution to unilateral problems associated to the equations of the type: Au + H(x, u, ∇u) − divφ(u) = µ ∈ L 1 (Ω) + W −1,p ′ (x) (Ω), where A is a Leray-Lions operator acting from W 1,p(x) 0 (Ω) into its dual W −1,p(x) (Ω), the nonlinear term H(x, s, ξ) satisfies some growth and the sign conditions and φ(u) ∈ C 0 (R, R N)