Positive solution of a singular non-linear elliptic boundary value problem

摘要

The singular elliptic boundary value problem:Δu+g(x)uα+h(x)u−β=0inΩ,u>0inΩ,u=0on∂Ωis considered in this paper, where α∈(0,1), β>0, Ω is a bounded region in RN with a smooth boundary. Under a set of suitable assumptions including that h(x)⩾0 in Ω and suppg−⊂⊂supph, it is proved that there exists a classic solution u, and when g(x)⩾0 (or g(x)⩽0) in whole Ω, then the solution u is unique.