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

Abstract

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, where Ω is a bounded domain with smooth boundary in RN, λ≥0, g∈C1((0,∞),(0,∞)), lims→0+g(s)=∞, b,a∈Clocα(Ω), are positive in Ω, may be vanishing or singular on the boundary, and f∈C([0,∞),[0,∞)). We reveal that the nonlinear term 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 a and b.