Second order expansion for the solution to a singular Dirichlet problem

Ling Mi and Bin Liu

Applied Mathematics and Computation, 2015, vol. 270, issue C, 401-412

Abstract: In this paper, we analyze the second order expansion for the unique solution near the boundary to the singular Dirichlet problem −▵u=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 lims→0+g(s)=∞ and g is normalized regularly varying at zero with index −γ (γ > 1), b∈Clocα(Ω) (0 < α < 1), is positive in Ω, may be vanishing or singular on the boundary and belongs to the Kato class K(Ω). Our analysis is based on the sub-supersolution method and Karamata regular variation theory.

Keywords: Semilinear elliptic equations; Singular Dirichlet problem; Second order expansion; Sub-supersolution method; Karamata regular variation theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:401-412

DOI: 10.1016/j.amc.2015.08.036

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