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Here $f :[0,\\infty) \\to [0,\\infty)$ is a continuous nondecreasing map satisfying $\\lim\\limits_{u\\to \\infty}\\frac{f(u)}{u^{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":"1801.06461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-19T15:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"dfe5ec841003c6cbc5a394a0f73795dc1c95fd5e4c50e74d80c03a4adb985293","abstract_canon_sha256":"cb9f29c4a0bbf37b17f2cacfaa15b155f9e1cdff4c3d4cc4128cc4c4767549d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:30.008518Z","signature_b64":"s6VI4nhiccQb7U1LpTxLbaQYpr5Z5tEQR6c+o2QtnZ9CV2Z4QDN6lhDK28nxLYGcRSIsxLu3JnUOYdAz7huZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e68f315538f6d613b04c7aa9793c9bd0507170b004a9f7bf7de9f69529af413","last_reissued_at":"2026-05-18T00:25:30.007799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:30.007799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of three positive solutions for a nonlocal singular dirichlet boundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Tuhina Mukherjee","submitted_at":"2018-01-19T15:28:06Z","abstract_excerpt":"In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem \\begin{equation*} (P_\\la)\\left\\{ \\begin{split} (-\\De)^su &= \\la\\frac{f(u)}{u^q}, \\; \\; u>0 \\;\\; \\text{in}\\;\\; \\Om,\\\\ u &= 0\\;\\; \\text{in}\\;\\; \\mb R^n \\setminus \\Om \\end{split} \\right. \\end{equation*} where $(-\\De)^s$ denotes the fractional Laplace operator for $s\\in (0,1)$, $n>2s$, $q \\in (0,1)$, $\\la>0$ and $\\Om$ is smooth bounded domain in $\\mb R^n$. 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