{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XTZS66KYHJCXBNAFJVJEPKKCGQ","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":"cc467e1e1fa98e0c3f5d0ace9c6633dbf4e59cb987e1d92f38fe24fa757d1914","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-21T08:08:26Z","title_canon_sha256":"576b4eeb59c9c71d62803ee69a1377c3f52df5e6ecc18ce44555d1195eebd8fd"},"schema_version":"1.0","source":{"id":"1105.4225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4225","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4225v1","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4225","created_at":"2026-05-18T04:21:29Z"},{"alias_kind":"pith_short_12","alias_value":"XTZS66KYHJCX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XTZS66KYHJCXBNAF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XTZS66KY","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:aad8ceda0e8d107676afa01596a63d806ee626a4a8396b81347aa89a1a12814b","target":"graph","created_at":"2026-05-18T04:21:29Z","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":"The main purpose of this paper is to show that there exists a positive number\n  $\\lambda_{1}$, the first eigenvalue, such that some $p(x)$-Laplace equation admits a solution if\n  $\\lambda=\\lambda_{1}$ and that\n  $\\lambda_{1}$ is simple, i.e., with respect to \\textit{the first eigenvalue} solutions, which are not equal to zero a. e., of the $p(x)$-Laplace equation forms an one dimensional subset. Furthermore, by developing Moser method we obtained some results concerning H\\\"{o}lder continuity and bounded properties of the solutions. Our works are done in the setting of the Generalized-Sobolev S","authors_text":"Yongqiang Fu, Yushan Jiang","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-21T08:08:26Z","title":"On the Eigenvalue of $p(x)$-Laplace Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4225","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":"sha256:77d23e106e16ad4dd14e43239d10fd6602f74c659e89f3fb5fa51eb62e6ccd6c","target":"record","created_at":"2026-05-18T04:21:29Z","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":"cc467e1e1fa98e0c3f5d0ace9c6633dbf4e59cb987e1d92f38fe24fa757d1914","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-21T08:08:26Z","title_canon_sha256":"576b4eeb59c9c71d62803ee69a1377c3f52df5e6ecc18ce44555d1195eebd8fd"},"schema_version":"1.0","source":{"id":"1105.4225","kind":"arxiv","version":1}},"canonical_sha256":"bcf32f79583a4570b4054d5247a942342c7e530ca87623a0874d2d5f2f00448b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcf32f79583a4570b4054d5247a942342c7e530ca87623a0874d2d5f2f00448b","first_computed_at":"2026-05-18T04:21:29.564242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:29.564242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yP8b1IuqnCbCiQF5/rx3PJu/9Zq3ONoWbu7Eiq4nN8Tv1qs41if8Y5KnPEjcY3Qd0RqK8AiNO177yuXP/5b+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:29.564627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77d23e106e16ad4dd14e43239d10fd6602f74c659e89f3fb5fa51eb62e6ccd6c","sha256:aad8ceda0e8d107676afa01596a63d806ee626a4a8396b81347aa89a1a12814b"],"state_sha256":"2b06b88c8ba882afd7e2c70cbde6dc7b417de756f1db764e7254dd1c96003cc2"}