A remark on the uniqueness of positive solutions for some Dirichlet problems Original Research Article

In this paper we prove the uniqueness of positive weak solutions to the problem View the MathML source-Δpu=g(x,u),x∈Ω,u=0,x∈∂Ω, Turn MathJax on by a direct argument. Here ΩΩ is a bounded domain in RN(N⩾3)RN(N⩾3) with smooth boundary ∂Ω∂Ω, ΔpΔp denotes the p-Laplacian operator defined by Δpz=div(|∇z|p-2∇z)Δpz=div(|∇z|p-2∇z); p>1p>1, g(x,0)=0g(x,0)=0, for a.e. x∈Ω,x∈Ω, and g(x,u)g(x,u) is a Caratheodory function. We provide a direct uniqueness proof for this problem, under certain conditions.