The second expansion of the solution for a singular elliptic boundary value problem

In this paper we analyze the second expansion of the unique solution near the boundary to the singular Dirichlet problem − 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 , ∞ ) ) , g is decreasing on ( 0 , ∞ ) with lim s → 0 + g ( s ) = ∞ and g is normalised regularly varying at zero with index −γ ( γ > 1 ), b ∈ C α ( Ω ¯ ) , is positive in Ω, may be vanishing on the boundary.