{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HUN5BT47VOM6IX6QTWZIC5A4H2","short_pith_number":"pith:HUN5BT47","schema_version":"1.0","canonical_sha256":"3d1bd0cf9fab99e45fd09db281741c3eb1b8872e9daa0e31d122b08319a9ed14","source":{"kind":"arxiv","id":"1502.06316","version":2},"attestation_state":"computed","paper":{"title":"Existence and multiplicity results for fractional $p$-Kirchhoff equation with sign changing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-02-23T05:20:24Z","abstract_excerpt":"In this paper, we show the existence and multiplicity of nontrivial, non-negative solutions of the fractional $p$-Kirchhoff problem  \\begin{equation*} \\begin{array}{rllll} M\\left(\\displaystyle\\int_{\\mathbb{R}^{2n}}\\frac{|u(x)-u(y)|^p}{\\left|x-y\\right|^{n+ps}}dx\\,dy\\right)(-\\Delta)^{s}_p u &=\\lambda f(x)|u|^{q-2}u+ g(x)\\left|u\\right|^{r-2}u\\, \\text{in} \\Omega,\\\\ u&=0 \\;\\mbox{in} \\mathbb{R}^{n}\\setminus \\Omega, \\end{array} \\end{equation*} where $(-\\Delta)^{s}_p$ is the fractional $p$-Laplace operator, $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary, $f \\in L^{\\frac{r}{r-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":"1502.06316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-23T05:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"c668eafeefe27feb5c532d620c43015f36b2d4fb1b6e4ab2398bc680a1c8e712","abstract_canon_sha256":"4e8882dbfd4cf7ecf4704a1ad01522ea02e36e87549a69c684564b6321d9f3fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.333553Z","signature_b64":"H6MrbZi3wV38nPPYjYGcCmTTNbXm+oOr+bEFZM9S2w2OqMIn1RRAkRgnVWcI5OjF8dxSpK60lnNNCbHvN2lYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d1bd0cf9fab99e45fd09db281741c3eb1b8872e9daa0e31d122b08319a9ed14","last_reissued_at":"2026-05-18T01:31:11.333077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.333077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and multiplicity results for fractional $p$-Kirchhoff equation with sign changing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-02-23T05:20:24Z","abstract_excerpt":"In this paper, we show the existence and multiplicity of nontrivial, non-negative solutions of the fractional $p$-Kirchhoff problem  \\begin{equation*} \\begin{array}{rllll} M\\left(\\displaystyle\\int_{\\mathbb{R}^{2n}}\\frac{|u(x)-u(y)|^p}{\\left|x-y\\right|^{n+ps}}dx\\,dy\\right)(-\\Delta)^{s}_p u &=\\lambda f(x)|u|^{q-2}u+ g(x)\\left|u\\right|^{r-2}u\\, \\text{in} \\Omega,\\\\ u&=0 \\;\\mbox{in} \\mathbb{R}^{n}\\setminus \\Omega, \\end{array} \\end{equation*} where $(-\\Delta)^{s}_p$ is the fractional $p$-Laplace operator, $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary, $f \\in L^{\\frac{r}{r-q}}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06316","kind":"arxiv","version":2},"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":"1502.06316","created_at":"2026-05-18T01:31:11.333146+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06316v2","created_at":"2026-05-18T01:31:11.333146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06316","created_at":"2026-05-18T01:31:11.333146+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUN5BT47VOM6","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUN5BT47VOM6IX6Q","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUN5BT47","created_at":"2026-05-18T12:29:25.134429+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/HUN5BT47VOM6IX6QTWZIC5A4H2","json":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2.json","graph_json":"https://pith.science/api/pith-number/HUN5BT47VOM6IX6QTWZIC5A4H2/graph.json","events_json":"https://pith.science/api/pith-number/HUN5BT47VOM6IX6QTWZIC5A4H2/events.json","paper":"https://pith.science/paper/HUN5BT47"},"agent_actions":{"view_html":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2","download_json":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2.json","view_paper":"https://pith.science/paper/HUN5BT47","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06316&json=true","fetch_graph":"https://pith.science/api/pith-number/HUN5BT47VOM6IX6QTWZIC5A4H2/graph.json","fetch_events":"https://pith.science/api/pith-number/HUN5BT47VOM6IX6QTWZIC5A4H2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2/action/storage_attestation","attest_author":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2/action/author_attestation","sign_citation":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2/action/citation_signature","submit_replication":"https://pith.science/pith/HUN5BT47VOM6IX6QTWZIC5A4H2/action/replication_record"}},"created_at":"2026-05-18T01:31:11.333146+00:00","updated_at":"2026-05-18T01:31:11.333146+00:00"}