Boundary behavior of large solutions to p-Laplacian elliptic equations

This paper is concerned with exact asymptotic behavior near the boundary of large solutions to quasilinear elliptic equations △pu(x)=b(x)f(u(x)),x∈Ω, where Ω is a bounded smooth domain in RN, △pu=div(|∇u|p−2∇u) with p>1, and b∈C(Ω) is nonnegative in Ω, but may be vanishing or appropriately singular (including critical singular) on the boundary. We give one new condition near infinity on f which plays a crucial role in the boundary behavior of solutions.