{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GHWUKGUPUX7R65CSHJZDN7RRNY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"26a3c51aecdf66b40f61562d5e2314ae8d0f31ba20ff864d11654615578910fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-03T02:55:16Z","title_canon_sha256":"c4ffc8b907ee1fa79e6672c0fa93b2e7021426544cab8e17d4115b91a596bcaa"},"schema_version":"1.0","source":{"id":"1607.00584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00584","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00584v1","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00584","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"GHWUKGUPUX7R","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GHWUKGUPUX7R65CS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GHWUKGUP","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:f03233656b758c3095741492f52c589a68bd026330403db97dc32abeeb9928ec","target":"graph","created_at":"2026-05-18T01:11:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Chunshan Zhao, Jinghua Yao, Li Yin, Qihu Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-03T02:55:16Z","title":"Multiple solutions with constant sign of a Dirichlet problem for a class of elliptic systems with variable exponent growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00584","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e1dc4154f10fcfdd288f6ebcf7b8c19ddfdede60f19415686400c4aac1195b6e","target":"record","created_at":"2026-05-18T01:11:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"26a3c51aecdf66b40f61562d5e2314ae8d0f31ba20ff864d11654615578910fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-03T02:55:16Z","title_canon_sha256":"c4ffc8b907ee1fa79e6672c0fa93b2e7021426544cab8e17d4115b91a596bcaa"},"schema_version":"1.0","source":{"id":"1607.00584","kind":"arxiv","version":1}},"canonical_sha256":"31ed451a8fa5ff1f74523a7236fe316e178ba95a626b49767b390d172a9ee218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ed451a8fa5ff1f74523a7236fe316e178ba95a626b49767b390d172a9ee218","first_computed_at":"2026-05-18T01:11:34.683302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:34.683302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pz+hvS4ACCWRi+Y5pVk98ClAUuQYkCP6zFQee2c2IbvS6GCBINyb7rmrJrRBrk72AIUZVwkMrJz7kghH2BHWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:34.683751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dc4154f10fcfdd288f6ebcf7b8c19ddfdede60f19415686400c4aac1195b6e","sha256:f03233656b758c3095741492f52c589a68bd026330403db97dc32abeeb9928ec"],"state_sha256":"ddbead8544a52a72919c03efd911277938f5d242c487778817fa150b7a37d055"}