We study in the framework of Orlicz Sobolev spaces W 1 0 L M (Ω), the existence of entropic solutions to the nonlinear elliptic problems: − div a(x, u, ∇u) + div φ(u) = f in Ω, for the case where the second member of the equation f ∈ L 1 (Ω), and φ ∈ (C 0 (R)) N .
The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the Δ2-condition. The source term is merely integrable.
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