Nonlinear elliptic equations with measure data in Musielak-Orlicz spaces

Abstract

In this paper we will prove the existence of solutions of the unilateral problem

Au - div Φ(x,u) + H(x, u, ∇ u) = μ

in Musielak spaces, where A is a Leray-Lions operator defined on D(A) ⊂ W₀¹ L_M (Ω), μ ∈ L(Ω) + W^-1 E_M'(Ω), where M and M' are two complementary Musielak-Orlicz functions and both the first and the second lower terms Φ and H satisfies only the growth condition and u ≥ ζ where ζ is a measurable function.