{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EJLRJMZLHBW3JW2VI72GR2H2VO","short_pith_number":"pith:EJLRJMZL","schema_version":"1.0","canonical_sha256":"225714b32b386db4db5547f468e8faaba712483acd89ae409e0aff710922c440","source":{"kind":"arxiv","id":"1703.08404","version":1},"attestation_state":"computed","paper":{"title":"Sign changing solutions of p-fractional equations with concave-convex nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta","submitted_at":"2017-03-24T13:30:58Z","abstract_excerpt":"In this article we study the existence of sign changing solution of the following p-fractional problem with concave-critical nonlinearities: \\begin{eqnarray*}\n  (-\\Delta)^s_pu &=& \\mu |u|^{q-1}u + |u|^{p^*_s-2}u \\quad\\mbox{in}\\quad \\Omega, u&=&0\\quad\\mbox{in}\\quad\\mathbb{R}^N\\setminus\\Omega, \\end{eqnarray*} where $s\\in(0,1)$ and $p\\geq 2$ are fixed parameters, $0<q<p-1$, $\\mu\\in\\mathbb{R}^+$ and $p_s^*=\\frac{Np}{N-ps}$. $\\Omega$ is an open, bounded domain in $\\mathbb{R}^N$ with smooth boundary with $N>ps$ ."},"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":"1703.08404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-24T13:30:58Z","cross_cats_sorted":[],"title_canon_sha256":"ed870f5378be67f0ac0a3df24c2a9059ca51da6983a18da851e7fdd626c1df84","abstract_canon_sha256":"aba2222f360077650f740c5e9fbc231c239551fd2c31f0db0e9d0b50498a6072"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:34.527846Z","signature_b64":"H9dGPR3Kdv5nSvZ1B1vvm0YZHFD52ye+fK7uhdac8xv1cmV1VeRrv5FZ8hxVbjlPhiIcLKmElajUIhxAmYO7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"225714b32b386db4db5547f468e8faaba712483acd89ae409e0aff710922c440","last_reissued_at":"2026-05-18T00:25:34.527087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:34.527087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign changing solutions of p-fractional equations with concave-convex nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta","submitted_at":"2017-03-24T13:30:58Z","abstract_excerpt":"In this article we study the existence of sign changing solution of the following p-fractional problem with concave-critical nonlinearities: \\begin{eqnarray*}\n  (-\\Delta)^s_pu &=& \\mu |u|^{q-1}u + |u|^{p^*_s-2}u \\quad\\mbox{in}\\quad \\Omega, u&=&0\\quad\\mbox{in}\\quad\\mathbb{R}^N\\setminus\\Omega, \\end{eqnarray*} where $s\\in(0,1)$ and $p\\geq 2$ are fixed parameters, $0<q<p-1$, $\\mu\\in\\mathbb{R}^+$ and $p_s^*=\\frac{Np}{N-ps}$. $\\Omega$ is an open, bounded domain in $\\mathbb{R}^N$ with smooth boundary with $N>ps$ ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08404","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":"1703.08404","created_at":"2026-05-18T00:25:34.527218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08404v1","created_at":"2026-05-18T00:25:34.527218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08404","created_at":"2026-05-18T00:25:34.527218+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJLRJMZLHBW3","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJLRJMZLHBW3JW2V","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJLRJMZL","created_at":"2026-05-18T12:31:12.930513+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/EJLRJMZLHBW3JW2VI72GR2H2VO","json":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO.json","graph_json":"https://pith.science/api/pith-number/EJLRJMZLHBW3JW2VI72GR2H2VO/graph.json","events_json":"https://pith.science/api/pith-number/EJLRJMZLHBW3JW2VI72GR2H2VO/events.json","paper":"https://pith.science/paper/EJLRJMZL"},"agent_actions":{"view_html":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO","download_json":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO.json","view_paper":"https://pith.science/paper/EJLRJMZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08404&json=true","fetch_graph":"https://pith.science/api/pith-number/EJLRJMZLHBW3JW2VI72GR2H2VO/graph.json","fetch_events":"https://pith.science/api/pith-number/EJLRJMZLHBW3JW2VI72GR2H2VO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO/action/storage_attestation","attest_author":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO/action/author_attestation","sign_citation":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO/action/citation_signature","submit_replication":"https://pith.science/pith/EJLRJMZLHBW3JW2VI72GR2H2VO/action/replication_record"}},"created_at":"2026-05-18T00:25:34.527218+00:00","updated_at":"2026-05-18T00:25:34.527218+00:00"}