The existence and global optimal asymptotic behaviour of large solutions for a semilinear elliptic problem

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k(x)g(u), u > 0, x ∈ ω, u|δ ω = +∞, where ω is a bounded domain with smooth boundary in , and there exists p > 1, such that is non-negative non-trivial in Ω which may be singular on the boundary.