Uniqueness of boundary blowup solutions to -curvature equation

We consider the boundary blowup problem for the k -curvature equation, i.e., H k [ u ] = f ( u ) g ( | D u | ) in an n -dimensional domain Ω , with the boundary condition u ( x ) → ∞ as dist ( x , ∂ Ω ) → 0 . We prove the uniqueness result under some hypotheses.