{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XTZS66KYHJCXBNAFJVJEPKKCGQ","short_pith_number":"pith:XTZS66KY","schema_version":"1.0","canonical_sha256":"bcf32f79583a4570b4054d5247a942342c7e530ca87623a0874d2d5f2f00448b","source":{"kind":"arxiv","id":"1105.4225","version":1},"attestation_state":"computed","paper":{"title":"On the Eigenvalue of $p(x)$-Laplace Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Yongqiang Fu, Yushan Jiang","submitted_at":"2011-05-21T08:08:26Z","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"},"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":"1105.4225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-21T08:08:26Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"576b4eeb59c9c71d62803ee69a1377c3f52df5e6ecc18ce44555d1195eebd8fd","abstract_canon_sha256":"cc467e1e1fa98e0c3f5d0ace9c6633dbf4e59cb987e1d92f38fe24fa757d1914"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.564627Z","signature_b64":"yP8b1IuqnCbCiQF5/rx3PJu/9Zq3ONoWbu7Eiq4nN8Tv1qs41if8Y5KnPEjcY3Qd0RqK8AiNO177yuXP/5b+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf32f79583a4570b4054d5247a942342c7e530ca87623a0874d2d5f2f00448b","last_reissued_at":"2026-05-18T04:21:29.564242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.564242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Eigenvalue of $p(x)$-Laplace Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Yongqiang Fu, Yushan Jiang","submitted_at":"2011-05-21T08:08:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4225","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":"1105.4225","created_at":"2026-05-18T04:21:29.564306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4225v1","created_at":"2026-05-18T04:21:29.564306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4225","created_at":"2026-05-18T04:21:29.564306+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTZS66KYHJCX","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTZS66KYHJCXBNAF","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTZS66KY","created_at":"2026-05-18T12:26:47.523578+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/XTZS66KYHJCXBNAFJVJEPKKCGQ","json":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ.json","graph_json":"https://pith.science/api/pith-number/XTZS66KYHJCXBNAFJVJEPKKCGQ/graph.json","events_json":"https://pith.science/api/pith-number/XTZS66KYHJCXBNAFJVJEPKKCGQ/events.json","paper":"https://pith.science/paper/XTZS66KY"},"agent_actions":{"view_html":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ","download_json":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ.json","view_paper":"https://pith.science/paper/XTZS66KY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4225&json=true","fetch_graph":"https://pith.science/api/pith-number/XTZS66KYHJCXBNAFJVJEPKKCGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XTZS66KYHJCXBNAFJVJEPKKCGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ/action/storage_attestation","attest_author":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ/action/author_attestation","sign_citation":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ/action/citation_signature","submit_replication":"https://pith.science/pith/XTZS66KYHJCXBNAFJVJEPKKCGQ/action/replication_record"}},"created_at":"2026-05-18T04:21:29.564306+00:00","updated_at":"2026-05-18T04:21:29.564306+00:00"}