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 − Δ u = b ( x ) g ( u ) , u > 0 , x ∈ Ω , u | ∂ Ω = 0 , where Ω is a bounded domain with smooth boundary in R N , g ∈ C 1 ( ( 0 , ∞ ) , ( 0 , ∞ ) ) , lim s → 0 + g ( s ) = ∞ , g is decreasing on ( 0 , ∞ ) , which is rapidly varying or normalized regularly varying at zero, b ∈ C loc α ( Ω ) , is positive in Ω, may be vanishing or singular on the boundary and belongs to the Kato class K ( Ω ) .