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 −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,∞) with and g is normalised regularly varying at zero with index −γ (γ>1), , is positive in Ω, may be vanishing on the boundary.