Iterative solution for a singular nonlinear elliptic problem

摘要

We consider the singular boundary-value problem Δu+q(x)uα+p(x)u−γ=0inΩ,u|∂Ω=0, where 0<γ<1/N,0<α<1. Under the assumptions q(x)⩾0,p(x)⩾0 and p(x)+q(x)≠0, and certain smoothness assumptions, we show that there exists a unique classical positive solution u∗(x)∈C2+min(α,γ)(Ω)∩C1,r(Ω̄)(0