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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 $q$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.00388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-01T18:34:37Z","cross_cats_sorted":[],"title_canon_sha256":"83d1908a6ef91b18aec72c97c2e2eb80a908472e030d2d786d11723d2d71b8ee","abstract_canon_sha256":"2957bd2d444efa4c74597c1b617dec95a3064782df624a5051de480161770884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:51.041009Z","signature_b64":"jM83ydPz6KnbhI4GKK+LEOezBOXzNOY2n5wJuGMCdDE2928mNVSJku2aQUvYNGMkmEdXQ6ygQ0xqqdZ8ByJuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a04bdad41f7ef02333f5d716d2947e07258fa5e818c7f3e8a124396c4fa57c50","last_reissued_at":"2026-05-18T00:13:51.040229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:51.040229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $N>2s$. 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