{"paper":{"title":"Nonlinear fractional elliptic problem with singular term at the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Primo, Boumediene Abdellaoui, kheireddine Biroud","submitted_at":"2017-10-01T18:34:37Z","abstract_excerpt":"Let $\\Omega\\subset \\mathbb{R}^N$ be a bounded regular domain, $0<s<1$ and $N>2s$. We consider $$ (P)\\left\\{ \\begin{array}{rcll} (-\\Delta)^s u &= & \\frac{u^{q}}{d^{2s}} & \\text{ in }\\Omega , \\\\ u &> & 0 & \\text{in }\\Omega , \\\\ u & = & 0 & \\text{ in }\\mathbb{R}^N\\setminus\\Omega ,% \\end{array}% \\right. $$ where $0<q\\le 2^*_s-1$, $0<s<1$ and $d(x) = dist(x,\\partial\\Omega)$. {The main goal } of this paper is to analyze existence and non existence of solution to problem $(P)$ according to the value of $s$ and $q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00388","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}