This paper is devoted to the study of the following obstacle problem
−div(a(x,u,∇u))+g(x,u,∇u)=f in Ω,(1)
where Ω is an open bounded domain of ℝN(N≥2),a:Ω×ℝ×ℝN→ℝN is a Carathéodory function satisfying some growth, monotonicity and coerciveness conditions.
Under some suitable conditions on the function g and if f∈L1Ω, the authors prove the existence of entropy solutions to the problem (1) in the framework of generalized Soblev spaces with variable exponents using approximation and penalization methods.

generalized Sobolev spaces; boundary value problems; truncations; penalized equations