Nonlinear elliptic equations with a lower-order term depending on the gradient in Orlicz spaces.

In this paper, we prove an existence result of the entropy solution to some nonlinear elliptic Dirichlet problem defined on Orlicz–Sobolev spaces and whose simplest model is (1) - div A (| ∇ u |) ∇ u | ∇ u | 2 + α u = β (u) A (| ∇ u |) + f in Ω u = 0 on ∂ Ω , where A is a N -function, α > 0 is a real number, β is a real continuous function and f ∈ E A β (Ω) , with Ω is a bounded open in R N ( N ≥ 2 ), such that A β (s) = ∫ 0 s e ∫ 0 v β (η) d η - 1 d v . [ABSTRACT FROM AUTHOR]