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

Abstract

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 Δ u = 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 lim s → ∞ g ( S ξ ) g ( s ) = ξ p , ∀ ξ > 0 , a n d k ∈ C l o c α ( Ω ) is non-negative non-trivial in Ω which may be singular on the boundary.