{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LRE6RB5ERQOBSETP3VL2YM5D3V","short_pith_number":"pith:LRE6RB5E","schema_version":"1.0","canonical_sha256":"5c49e887a48c1c19126fdd57ac33a3dd67739cb92509b7c3bd07c1e435091d50","source":{"kind":"arxiv","id":"1511.03579","version":1},"attestation_state":"computed","paper":{"title":"Critical growth fractional systems with exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-11-11T17:12:14Z","abstract_excerpt":"We study the existence of positive solutions for the system of fractional elliptic equations of the type, \\begin{equation*} \\begin{array}{rl} (-\\Delta)^{\\frac{1}{2}} u &=\\frac{p}{p+q}\\lambda f(x)|u|^{p-2}u|v|^q + h_1(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\\\\ (-\\Delta)^{\\frac{1}{2}} v &=\\frac{q}{p+q}\\lambda f(x)|u|^p|v|^{q-2}v + h_2(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\n  u,v&>0 \\;\\textrm{in } \\; (-1,1),\n  u&=v=0 \\; \\text{in} \\; \\mathbb R\\setminus (-1,1).\n  \\end{array} \\end{equation*} where {$1<p+q<2$}, $h_1(u,v)=(\\alpha{+}2u^2)|u|^{\\alpha-2}u|v|^\\beta, h_2(u,v)=(\\beta{+}2v^2) |u|^\\alpha "},"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":"1511.03579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-11T17:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"900d0912c7bf1d0c01162b961544d0ed755832f554abe7d616d862569d253991","abstract_canon_sha256":"f7f6b93a436f58fcb2b0fade082278301257ae581dc976d52ed7d4fe9464dc1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:08.673965Z","signature_b64":"BeE+rGcbA1iBmSQMICtfVWWwslBI9ug8OeK/lDXQ6uKcNMeNzEkORBJMKHRpCZB2raQc+lngBj5sAC59hwbQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c49e887a48c1c19126fdd57ac33a3dd67739cb92509b7c3bd07c1e435091d50","last_reissued_at":"2026-05-18T01:27:08.673171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:08.673171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical growth fractional systems with exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-11-11T17:12:14Z","abstract_excerpt":"We study the existence of positive solutions for the system of fractional elliptic equations of the type, \\begin{equation*} \\begin{array}{rl} (-\\Delta)^{\\frac{1}{2}} u &=\\frac{p}{p+q}\\lambda f(x)|u|^{p-2}u|v|^q + h_1(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\\\\ (-\\Delta)^{\\frac{1}{2}} v &=\\frac{q}{p+q}\\lambda f(x)|u|^p|v|^{q-2}v + h_2(u,v) e^{u^2+v^2},\\;\\textrm{in}\\; (-1, 1),\n  u,v&>0 \\;\\textrm{in } \\; (-1,1),\n  u&=v=0 \\; \\text{in} \\; \\mathbb R\\setminus (-1,1).\n  \\end{array} \\end{equation*} where {$1<p+q<2$}, $h_1(u,v)=(\\alpha{+}2u^2)|u|^{\\alpha-2}u|v|^\\beta, h_2(u,v)=(\\beta{+}2v^2) |u|^\\alpha "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03579","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":"1511.03579","created_at":"2026-05-18T01:27:08.673285+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03579v1","created_at":"2026-05-18T01:27:08.673285+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03579","created_at":"2026-05-18T01:27:08.673285+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRE6RB5ERQOB","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRE6RB5ERQOBSETP","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRE6RB5E","created_at":"2026-05-18T12:29:29.992203+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/LRE6RB5ERQOBSETP3VL2YM5D3V","json":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V.json","graph_json":"https://pith.science/api/pith-number/LRE6RB5ERQOBSETP3VL2YM5D3V/graph.json","events_json":"https://pith.science/api/pith-number/LRE6RB5ERQOBSETP3VL2YM5D3V/events.json","paper":"https://pith.science/paper/LRE6RB5E"},"agent_actions":{"view_html":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V","download_json":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V.json","view_paper":"https://pith.science/paper/LRE6RB5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03579&json=true","fetch_graph":"https://pith.science/api/pith-number/LRE6RB5ERQOBSETP3VL2YM5D3V/graph.json","fetch_events":"https://pith.science/api/pith-number/LRE6RB5ERQOBSETP3VL2YM5D3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V/action/storage_attestation","attest_author":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V/action/author_attestation","sign_citation":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V/action/citation_signature","submit_replication":"https://pith.science/pith/LRE6RB5ERQOBSETP3VL2YM5D3V/action/replication_record"}},"created_at":"2026-05-18T01:27:08.673285+00:00","updated_at":"2026-05-18T01:27:08.673285+00:00"}