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.jrujp􀀀2ru/ D g.u/ 􀀀 b.x/f .u/ in where is a real number, and b.x/ > 0 in and vanishes on @ . The uniqueness of such a solution follows as a consequence of the exact blow-up rate.