Renormalized Solutions of Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

Abstract. The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems −div a(r, u,Δu) + φ(u) + g(x, u,Δu) = f − div F, in a bounded open set and u = 0 on @ , in the framework of Orlicz-Sobolev spaces without any restriction on the M N-function of the Orlicz spaces, where −div a(x, u,Δu) is a Leray-Lions operator defined from W10 LM(Ω) into its dual, φ ∈ C0(R,RN). The function g(x, u,Δu) is a non linear lower order term with natural growth with respect to |ru|, satisfying the sign condition and the datum μ is assumed to belong to L1(Ω) +W−1EM(Ω).