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\\text{in}\\;\\Omega \\\\ \\quad \\quad u, w>0\\;\\text{in}\\;\\Omega, \\quad u = w = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega, \\end{array} \\quad \\right. \\end{equation*} where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary $\\p"},"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":"1607.01150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-05T08:54:47Z","cross_cats_sorted":[],"title_canon_sha256":"ead5a855ab96434b334a227a65bdd070f5db0e047714e1d04f30e44cce8528f8","abstract_canon_sha256":"a70b1089724a2f6fc719ba75715a1ef02d6d6b4497763b9874aecb27cb654aab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:30.059670Z","signature_b64":"Ssz1FgI9iddTy35e/ptIhcjq222WcdIOrO4hnB+I4kaWWKkmiWUC9gcie0D8gpTZWYjxol4HvGrBxlkUvHr4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93bf0b54b276e31ca287259fddfbf42211271d68af0de1ea0930b51b655fc01a","last_reissued_at":"2026-05-18T01:11:30.059160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:30.059160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sarika Goyal","submitted_at":"2016-07-05T08:54:47Z","abstract_excerpt":"In this article, we study the following fractional-Laplacian system with singular nonlinearity \\begin{equation*} (P_{\\lambda,\\mu}) \\left\\{ \\begin{array}{lr} (-\\Delta)^s u = \\lambda f(x) u^{-q}+ \\frac{\\alpha}{\\alpha+\\beta}b(x) u^{\\alpha-1} w^\\beta\\; 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