The exact boundary behavior of solutions to singular nonlinear Lane–Emden–Fowler type boundary value problems

In this paper we analyze the exact boundary behavior of solutions to singular nonlinear Dirichlet problems −△u=b(x)g(u)+λa(x)f(u),u>0,x∈Ω,u|∂Ω=0−△u=b(x)g(u)+λa(x)f(u),u>0,x∈Ω,u|∂Ω=0, where ΩΩ is a bounded domain with smooth boundary in RNRN, λ≥0λ≥0, g∈C1((0,∞),(0,∞))g∈C1((0,∞),(0,∞)), lims→0+g(s)=∞lims→0+g(s)=∞, b,a∈Clocα(Ω), are positive in ΩΩ, may be vanishing or singular on the boundary, and f∈C([0,∞),[0,∞))f∈C([0,∞),[0,∞)). We reveal that the nonlinear term λa(x)f(u)λa(x)f(u) does not affect the first expansion of the classical solutions near the boundary to the problem for several kinds of functions aa and bb.