Abstract
We prove an existence result of solutions for nonlinear elliptic unilateral problems having natural growth terms and L1 data in Musielak-Orlicz-Sobolev space W1Lφ, under the assumption that the conjugate function of φ satisfies the ∆2-condition.
Highlights
On Orlicz spaces and in the variational case, it is well known that Gossez and Mustonen solved in [20] the following obstacle problem u ∈ Kφ
In the framework of variable exponent Sobolev spaces, Azroul, Redwane and Yazough have shown in [6] the existence of solutions for the unilateral problem associated to (1.1) where the second member f is in L1(Ω)
In the setting of Musielak-Orlicz spaces and in variational case, Benkirane and Sidi El vally [12] proved the existence of solutions for the obstacle problem (1.2), they generalized the work of Gossez and Mustonen in [20]
Summary
These functionals are convex modular and a norm on W 1Lφ(Ω) respectively
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