{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GHWUKGUPUX7R65CSHJZDN7RRNY","short_pith_number":"pith:GHWUKGUP","schema_version":"1.0","canonical_sha256":"31ed451a8fa5ff1f74523a7236fe316e178ba95a626b49767b390d172a9ee218","source":{"kind":"arxiv","id":"1607.00584","version":1},"attestation_state":"computed","paper":{"title":"Multiple solutions with constant sign of a Dirichlet problem for a class of elliptic systems with variable exponent growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunshan Zhao, Jinghua Yao, Li Yin, Qihu Zhang","submitted_at":"2016-07-03T02:55:16Z","abstract_excerpt":"We investigate the following Dirichlet problem with variable exponents: \\begin{equation*} \\left\\{ \\begin{array}{l} -\\bigtriangleup _{p(x)}u=\\lambda \\alpha (x)\\left\\vert u\\right\\vert ^{\\alpha (x)-2}u\\left\\vert v\\right\\vert ^{\\beta (x)}+F_{u}(x,u,v),\\text{ in }\\Omega , \\\\ -\\bigtriangleup _{q(x)}v=\\lambda \\beta (x)\\left\\vert u\\right\\vert ^{\\alpha (x)}\\left\\vert v\\right\\vert ^{\\beta (x)-2}v+F_{v}(x,u,v),\\text{ in }\\Omega , \\\\ u=0=v,\\text{ on }\\partial \\Omega. \\end{array} \\right. \\end{equation*} We present here, in the system setting, a new set of growth conditions under which we manage to use a no"},"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":"1607.00584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-03T02:55:16Z","cross_cats_sorted":[],"title_canon_sha256":"c4ffc8b907ee1fa79e6672c0fa93b2e7021426544cab8e17d4115b91a596bcaa","abstract_canon_sha256":"26a3c51aecdf66b40f61562d5e2314ae8d0f31ba20ff864d11654615578910fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:34.683751Z","signature_b64":"Pz+hvS4ACCWRi+Y5pVk98ClAUuQYkCP6zFQee2c2IbvS6GCBINyb7rmrJrRBrk72AIUZVwkMrJz7kghH2BHWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ed451a8fa5ff1f74523a7236fe316e178ba95a626b49767b390d172a9ee218","last_reissued_at":"2026-05-18T01:11:34.683302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:34.683302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple solutions with constant sign of a Dirichlet problem for a class of elliptic systems with variable exponent growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunshan Zhao, Jinghua Yao, Li Yin, Qihu Zhang","submitted_at":"2016-07-03T02:55:16Z","abstract_excerpt":"We investigate the following Dirichlet problem with variable exponents: \\begin{equation*} \\left\\{ \\begin{array}{l} -\\bigtriangleup _{p(x)}u=\\lambda \\alpha (x)\\left\\vert u\\right\\vert ^{\\alpha (x)-2}u\\left\\vert v\\right\\vert ^{\\beta (x)}+F_{u}(x,u,v),\\text{ in }\\Omega , \\\\ -\\bigtriangleup _{q(x)}v=\\lambda \\beta (x)\\left\\vert u\\right\\vert ^{\\alpha (x)}\\left\\vert v\\right\\vert ^{\\beta (x)-2}v+F_{v}(x,u,v),\\text{ in }\\Omega , \\\\ u=0=v,\\text{ on }\\partial \\Omega. \\end{array} \\right. \\end{equation*} We present here, in the system setting, a new set of growth conditions under which we manage to use a no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00584","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":"1607.00584","created_at":"2026-05-18T01:11:34.683374+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.00584v1","created_at":"2026-05-18T01:11:34.683374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00584","created_at":"2026-05-18T01:11:34.683374+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHWUKGUPUX7R","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHWUKGUPUX7R65CS","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHWUKGUP","created_at":"2026-05-18T12:30:19.053100+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/GHWUKGUPUX7R65CSHJZDN7RRNY","json":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY.json","graph_json":"https://pith.science/api/pith-number/GHWUKGUPUX7R65CSHJZDN7RRNY/graph.json","events_json":"https://pith.science/api/pith-number/GHWUKGUPUX7R65CSHJZDN7RRNY/events.json","paper":"https://pith.science/paper/GHWUKGUP"},"agent_actions":{"view_html":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY","download_json":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY.json","view_paper":"https://pith.science/paper/GHWUKGUP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.00584&json=true","fetch_graph":"https://pith.science/api/pith-number/GHWUKGUPUX7R65CSHJZDN7RRNY/graph.json","fetch_events":"https://pith.science/api/pith-number/GHWUKGUPUX7R65CSHJZDN7RRNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY/action/storage_attestation","attest_author":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY/action/author_attestation","sign_citation":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY/action/citation_signature","submit_replication":"https://pith.science/pith/GHWUKGUPUX7R65CSHJZDN7RRNY/action/replication_record"}},"created_at":"2026-05-18T01:11:34.683374+00:00","updated_at":"2026-05-18T01:11:34.683374+00:00"}