The boundary behavior of the unique solution to a singular Dirichlet problem

In this paper we analyze the boundary behavior of the unique solution to the singular Dirichlet problem for a Lane–Emden–Fowler equation −Δu=b(x)g(u), u>0, x∈Ω, u|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN, g∈C1((0,∞),(0,∞)), , g is decreasing on (0,∞), which is rapidly varying or normalized regularly varying at zero, , is positive in Ω, may be vanishing or singular on the boundary and belongs to the Kato class K(Ω).