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Sreenadh, Tuhina Mukherjee","submitted_at":"2018-06-16T01:39:12Z","abstract_excerpt":"In this article, we show the global multiplicity result for the following nonlocal singular problem \\begin{equation*}\n  (P_\\la):\\;\\quad (-\\De)^s u = u^{-q} + \\la u^{{2^*_s}-1}, \\quad u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om, \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > 2s,\\; s \\in (0,1),\\; \\la >0,\\; q>0$ satisfies $q(2s-1)<(2s+1)$ and $2^*_s=\\frac{2n}{n-2s}$. Employing the variational method, we show the existence of at least two distinct weak positive solutions for $(P_\\la)$ in $X_0$ when $\\la \\in (0,\\La)"},"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":"1806.06167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-16T01:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"4f16d99439c71023a947d5d6b6e42b7ed58912efa9695506b37cd0eb799aa87c","abstract_canon_sha256":"9c8b08b1e71b2a527c224aca8c11504d623aebcf77eb274afc1a2c4e680d3802"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:03.478766Z","signature_b64":"lIikF5Nkm2IBXq02UL/zcqeSXJAgvq7dsX5MJfqhMggfL7DXiOv25sP6iwnJab7sPrl6ajeD2lykUFjoc8SADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a6f254048aa5c89ca0eebdd7b56be938ac720f690219f6a57965e3af6ec07e1","last_reissued_at":"2026-05-18T00:13:03.478165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:03.478165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Global multiplicity result for a very singular critical nonlocal equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K. Sreenadh, Tuhina Mukherjee","submitted_at":"2018-06-16T01:39:12Z","abstract_excerpt":"In this article, we show the global multiplicity result for the following nonlocal singular problem \\begin{equation*}\n  (P_\\la):\\;\\quad (-\\De)^s u = u^{-q} + \\la u^{{2^*_s}-1}, \\quad u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om, \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > 2s,\\; s \\in (0,1),\\; \\la >0,\\; q>0$ satisfies $q(2s-1)<(2s+1)$ and $2^*_s=\\frac{2n}{n-2s}$. Employing the variational method, we show the existence of at least two distinct weak positive solutions for $(P_\\la)$ in $X_0$ when $\\la \\in (0,\\La)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06167","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.06167","created_at":"2026-05-18T00:13:03.478250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.06167v1","created_at":"2026-05-18T00:13:03.478250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06167","created_at":"2026-05-18T00:13:03.478250+00:00"},{"alias_kind":"pith_short_12","alias_value":"DJXSKQCIVJOI","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DJXSKQCIVJOITSQO","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DJXSKQCI","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO","json":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO.json","graph_json":"https://pith.science/api/pith-number/DJXSKQCIVJOITSQO5POXWVV6SO/graph.json","events_json":"https://pith.science/api/pith-number/DJXSKQCIVJOITSQO5POXWVV6SO/events.json","paper":"https://pith.science/paper/DJXSKQCI"},"agent_actions":{"view_html":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO","download_json":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO.json","view_paper":"https://pith.science/paper/DJXSKQCI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.06167&json=true","fetch_graph":"https://pith.science/api/pith-number/DJXSKQCIVJOITSQO5POXWVV6SO/graph.json","fetch_events":"https://pith.science/api/pith-number/DJXSKQCIVJOITSQO5POXWVV6SO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO/action/storage_attestation","attest_author":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO/action/author_attestation","sign_citation":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO/action/citation_signature","submit_replication":"https://pith.science/pith/DJXSKQCIVJOITSQO5POXWVV6SO/action/replication_record"}},"created_at":"2026-05-18T00:13:03.478250+00:00","updated_at":"2026-05-18T00:13:03.478250+00:00"}