The second order expansion of solutions to a singular Dirichlet boundary value problem

Abstract

Please cite this article in press as: H. Wan, The second order expansion of solutions to a singular Dirichlet boundary value problem, AbstractIn this paper, we mainly study the second order expansion of classical solutions in a neighborhoodwhere Ω is a bounded domain with smooth boundary in R N , λ ≥ 0. The weight functions b, a ∈ C α loc (Ω) are positive in Ω and both may be vanishing or be singular on the boundary. The function g ∈ C 1 ((0, ∞), (0, ∞)) satisfies lim t→0 + g(t) = ∞, and f ∈ C([0, ∞), [0, ∞)). We show that the nonlinear term λa(x)f (u) does not affect the second order expansion of solutions in a neighborhood of ∂Ω to the problem for some kinds of functions b and a.