Boundary asymptotic behavior and uniqueness of large solutions to quasilinear elliptic equations

We study the existence, uniqueness and exact asymptotic behavior of solutions near the boundary to a class of quasilinear elliptic equations −div(|∇u|p−2∇u)=λg(u)−b(x)f(u)inΩ where λλ is a real number, and b(x)>0b(x)>0 in ΩΩ and vanishes on ∂Ω∂Ω. The uniqueness of such a solution follows as a consequence of the exact blow-up rate.