Existence and Regularity of Solutions for Unbounded Elliptic Equations with Singular Nonlinearities

For q , γ > 0 , we study existence and regularity of solutions for unbounded elliptic problems whose simplest model is − div 1 + u q ∇ u = f / u γ in  Ω u = 0 on  ∂ Ω , where f ∈ L m Ω , m ≥ 1 .