{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7SFM2FLIMFGTYYQFQMO7LPQOPR","short_pith_number":"pith:7SFM2FLI","schema_version":"1.0","canonical_sha256":"fc8acd1568614d3c6205831df5be0e7c7ffb632270e4b13491d746e803ed9d34","source":{"kind":"arxiv","id":"1903.05346","version":1},"attestation_state":"computed","paper":{"title":"On a class of quasilinear elliptic equation with indefinite weights on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guoqing Zhang, Shoudong Man","submitted_at":"2019-03-13T07:53:03Z","abstract_excerpt":"Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $\\Omega\\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \\left \\{ \\begin{array}{lcr} -\\Delta_{p}u= \\lambda K(x)|u|^{p-2}u+f(x,u), \\ \\ x\\in\\Omega^{\\circ},\n  u=0, \\ \\ x\\in\\partial \\Omega, \\\\ \\end{array} \\right. $$ where $\\Omega^{\\circ}$ and $\\partial \\Omega$ denote the interior and the boundary of $\\Omega$ respectively, $\\Delta_{p}$ is the discrete $p$-Laplacian, $K(x)$ is a given function which may change sign, $\\lambda$ is the eigenval"},"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":"1903.05346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-13T07:53:03Z","cross_cats_sorted":[],"title_canon_sha256":"fe1cb7f34e90645dd7bc9ddeb17981f8dbcf3e3e6c44c0438712d93ee1191d24","abstract_canon_sha256":"74b1d56e5fb902d57485c15f695cad0978161e344ceca824830a4c27ef4e4c2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:24.574780Z","signature_b64":"o+nQR7jvxMsoiYGr0Aoag5zATtXK8ccCyiepE5qpIDNqBRcA8GyqRlO0B9vW81P0kqFhdbhxdU051NXbtFNLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc8acd1568614d3c6205831df5be0e7c7ffb632270e4b13491d746e803ed9d34","last_reissued_at":"2026-05-17T23:51:24.574014Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:24.574014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a class of quasilinear elliptic equation with indefinite weights on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guoqing Zhang, Shoudong Man","submitted_at":"2019-03-13T07:53:03Z","abstract_excerpt":"Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $\\Omega\\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \\left \\{ \\begin{array}{lcr} -\\Delta_{p}u= \\lambda K(x)|u|^{p-2}u+f(x,u), \\ \\ x\\in\\Omega^{\\circ},\n  u=0, \\ \\ x\\in\\partial \\Omega, \\\\ \\end{array} \\right. $$ where $\\Omega^{\\circ}$ and $\\partial \\Omega$ denote the interior and the boundary of $\\Omega$ respectively, $\\Delta_{p}$ is the discrete $p$-Laplacian, $K(x)$ is a given function which may change sign, $\\lambda$ is the eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05346","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":"1903.05346","created_at":"2026-05-17T23:51:24.574136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.05346v1","created_at":"2026-05-17T23:51:24.574136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05346","created_at":"2026-05-17T23:51:24.574136+00:00"},{"alias_kind":"pith_short_12","alias_value":"7SFM2FLIMFGT","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7SFM2FLIMFGTYYQF","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7SFM2FLI","created_at":"2026-05-18T12:33:12.712433+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/7SFM2FLIMFGTYYQFQMO7LPQOPR","json":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR.json","graph_json":"https://pith.science/api/pith-number/7SFM2FLIMFGTYYQFQMO7LPQOPR/graph.json","events_json":"https://pith.science/api/pith-number/7SFM2FLIMFGTYYQFQMO7LPQOPR/events.json","paper":"https://pith.science/paper/7SFM2FLI"},"agent_actions":{"view_html":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR","download_json":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR.json","view_paper":"https://pith.science/paper/7SFM2FLI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.05346&json=true","fetch_graph":"https://pith.science/api/pith-number/7SFM2FLIMFGTYYQFQMO7LPQOPR/graph.json","fetch_events":"https://pith.science/api/pith-number/7SFM2FLIMFGTYYQFQMO7LPQOPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR/action/storage_attestation","attest_author":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR/action/author_attestation","sign_citation":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR/action/citation_signature","submit_replication":"https://pith.science/pith/7SFM2FLIMFGTYYQFQMO7LPQOPR/action/replication_record"}},"created_at":"2026-05-17T23:51:24.574136+00:00","updated_at":"2026-05-17T23:51:24.574136+00:00"}