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Dhanya, Sweta Tiwari","submitted_at":"2019-05-24T07:06:16Z","abstract_excerpt":"In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type\n  $$ (P_\\lambda^\\mu)\\left\\{ \\begin{array}{lll} (-\\Delta)^s u&=& \\lambda(u^{q}-1)+\\mu u^r \\mbox{ in } \\Omega\\\\ u&>&0 \\mbox{ in } \\Omega\\\\ u&\\equiv &0 \\mbox{ on }{\\mathbb R^N\\setminus\\Omega}. \\end{array}\\right. $$ when the positive parameters $\\lambda$ and $\\mu$ belongs to certain range. Here $\\Omega\\subset\\mathbb R^N$ is assumed to be a bounded open set with smooth boundary, $s\\in (0,1), N> 2s$ and $0<q<1<r\\leq \\frac{N+2s}{N- 2s}.$ The proof relies on the construction of a positi"},"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":"1905.10062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T07:06:16Z","cross_cats_sorted":[],"title_canon_sha256":"a36e1fc185910d1a8fb59375459ec148ee68b78a7d2f7c0707380888a13f19d0","abstract_canon_sha256":"781c8f1a1f2a2ff71e43b58cb68e67785d67ae346abbbf9d6325e4b7cb9c6207"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:11.528477Z","signature_b64":"w227xCEe0esJIfhA22eoiWiXOXmi/aMlSBrkj49PUww5UykOzyPLm+Qo1yX6UO0A3QVDyWte140rXRgOsT+VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1a3f10accbad3d4df0452c52478ffb75984f3c95e50b9c01ed77dbf5833f78c","last_reissued_at":"2026-05-17T23:45:11.527923Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:11.527923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A multiparameter semipositone fractional laplacian problem involving critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"R. Dhanya, Sweta Tiwari","submitted_at":"2019-05-24T07:06:16Z","abstract_excerpt":"In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type\n  $$ (P_\\lambda^\\mu)\\left\\{ \\begin{array}{lll} (-\\Delta)^s u&=& \\lambda(u^{q}-1)+\\mu u^r \\mbox{ in } \\Omega\\\\ u&>&0 \\mbox{ in } \\Omega\\\\ u&\\equiv &0 \\mbox{ on }{\\mathbb R^N\\setminus\\Omega}. \\end{array}\\right. $$ when the positive parameters $\\lambda$ and $\\mu$ belongs to certain range. 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