{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z5YD2YEYMX6KHLBTJGMVQHHGKA","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":"b9f26715c9fa3e4b802e145779b01f3907a396d47994ba42cfa35bd2a81cc13f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T01:26:34Z","title_canon_sha256":"c9c4768d9404e3a7548ba062f941f0efefd02cb49b868ad6bbf47b7fb21dde5d"},"schema_version":"1.0","source":{"id":"1603.05329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05329","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05329v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05329","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z5YD2YEYMX6K","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5YD2YEYMX6KHLBT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5YD2YEY","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:48c7a55a7334d3c0a01e910c923393c12b21ba0573f46e6c8d91117b11f2a027","target":"graph","created_at":"2026-05-18T01:18:56Z","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 study the global solution curves, and prove the existence of infinitely many positive solutions for three classes of self-similar equations, with $p$-Laplace operator. In case $p=2$, these are well-known problems involving the Gelfand equation, the equation modeling electrostatic micro-electromechanical systems (MEMS), and a polynomial nonlinearity. We extend the classical results of D.D. Joseph and T.S. Lundgren \\cite{JL} to the case $p \\ne 2$, and we generalize the main result of Z. Guo and J. Wei \\cite{GW} on the equation modeling MEMS.","authors_text":"Philip Korman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T01:26:34Z","title":"Infinitely many solutions for three classes of self-similar equations, with the $p$-Laplace operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05329","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":"sha256:5fc9be038b510ed07ac50c6d2cde4246f7fae208e7a6f9bb87723395faa2c53b","target":"record","created_at":"2026-05-18T01:18:56Z","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":"b9f26715c9fa3e4b802e145779b01f3907a396d47994ba42cfa35bd2a81cc13f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T01:26:34Z","title_canon_sha256":"c9c4768d9404e3a7548ba062f941f0efefd02cb49b868ad6bbf47b7fb21dde5d"},"schema_version":"1.0","source":{"id":"1603.05329","kind":"arxiv","version":1}},"canonical_sha256":"cf703d609865fca3ac334999581ce6500a80c07975ad52b699072a6b4fe76941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf703d609865fca3ac334999581ce6500a80c07975ad52b699072a6b4fe76941","first_computed_at":"2026-05-18T01:18:56.637384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.637384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDwW6EQEVRIGeSSv6kZ6DOf/1zDX00CG+CdDqJu4Zq503uUcDSOts8lQHToMoIrH7sKVrhEPcuvlL6qz8TiRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.637778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fc9be038b510ed07ac50c6d2cde4246f7fae208e7a6f9bb87723395faa2c53b","sha256:48c7a55a7334d3c0a01e910c923393c12b21ba0573f46e6c8d91117b11f2a027"],"state_sha256":"9cbd09033b19e6b70c30015b59804f451c5d7a56ec3526969a6ac65ee9fc688e"}