Existence of renormalized solutions for some strongly nonlinear elliptic equations in Orlicz spaces

Abstract

Abstract We prove the existence of a renormalized solution for the Dirichlet problem associated to the nonlinear elliptic equations div a(x,u,∇u) - div Φ(u) + g(x,u,∇u) = f in Ω, in the general setting of Orlicz spaces, where Φ ∈ 𝒞0(ℝ,ℝ N ), the function g has a natural growth with respect to its third argument and satisfies the sign condition while the datum f belongs to W -1 E M¯(Ω). No Δ2-condition is needed for the considered N-functions.