Boundary Poisson Barriers and a Sharper Continuation Theorem for Li–Lin’s Problem

We sharpen the continuation part of Tang and Tang’s subsupersolution argument for the boundary singular Hardy–Sobolev equation −Δu=−λx−s1up−1+x−s2uq−1 in Ω,u=0 on ∂Ω, with 0∈∂Ω. Their explicit supersolution Mx−α forces the bulk superharmonicity restriction α≤N−2, hence the condition q≤p−s2−s1/N−2. We replace that bulk barrier by Poisson lifts of localized singular boundary data. For every 0 0 and s2−s1/p−q