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Abstract In this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form -∑i=1N∂iai(x,u,∇u)-∑i=1N∂iφi(u)=f, $$ - \sum\limits_{i = 1}^N {{\partial _i}{a_i}(x,u,\nabla u) - } \sum\limits_{i = 1}^N {{\partial _i}{\phi _i}(u) = f,} $$ where the right hand side f belongs to L1(Ω). The operator -∑i=1N∂iai(x,u,∇u) $- \sum\nolimits_{i = 1}^N {{\partial _i}{a_i}\left( {x,u,\nabla u} \right)} $ is a Leray-Lions anisotropic operator and ϕi ∈ C0(ℝ,ℝ).

Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms