A boundary blow-up elliptic problem with an inhomogeneous term

By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem Delta u = b(x)g(u) + lambda(x), it > 0 in Omega, u|partial derivative Omega = infinity, where Omega is a bounded domain with smooth boundary in R-N, lambda > 0, g is an element of C-1 [0, infinity) is increasing on [0, infinity), g(0) = 0, g' is regularly varying at infinity with positive index rho, the weight b, which is non-trivial and non-negative in Omega, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Omega and may be singular on the boundary. (C) 2007 Elsevier Ltd. All rights reserved.