Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f in Ω, u=0 on ∂Ω,}, where 00 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.