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Second order expansion for the solution to a singular Dirichlet problem

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  • Mi, Ling
  • Liu, Bin

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.

Suggested Citation

  • Mi, Ling & Liu, Bin, 2015. "Second order expansion for the solution to a singular Dirichlet problem," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 401-412.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:401-412
    DOI: 10.1016/j.amc.2015.08.036
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