Entropy Solutions to a Strongly Nonlinear Unilateral Obstacle Elliptic Problem with Orlicz Growth

In this paper , we investigate an existence result of solutions for the nonlinear elliptic unilateral problem {u ≥ ψ a.e. in Ω, Tk (u) ∈ W1 0 LM(Ω), ∫Ω A(x, u,∇u)∇Tk (u − ϕ) dx + ∫ Ω ϕ(x, u)∇Tk (u − ϕ) dx ≤ ∫ Ω f Tk (u − ϕ) dx, ∀ϕ ∈ L∞ (Ω) ∩ (Kψ = { u ∈ W1 0 LM(Ω) : u ≥ ψ a.e. in Ω } ) , where the lower-order term ϕ verifies a generalized natural growth condition described by a suitable N-function M and the data f is an element of L1(Ω). No restriction is assumed neither on M nor on its conjugate M.