Existence results for some unilateral problems without sign condition with obstacle free in Orlicz spaces Original Research Article

We prove the existence results in the setting of Orlicz spaces for the unilateral problem associated to the following equation, Au+g(x,u,∇u)=f,Au+g(x,u,∇u)=f, Turn MathJax on where AA is a Leray–Lions operator acting from its domain View the MathML sourceD(A)⊂W01LM(Ω) into its dual, while g(x,u,∇u)g(x,u,∇u) is a nonlinear term having a growth conditions with respect to ∇u∇u and no growth with respect to uu, but does not satisfy any sign condition. The right-hand side ff belongs to L1(Ω)L1(Ω), and the obstacle is a measurable function.