{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7VUAK2IUBLQINFDRA4QY5TAPUA","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":"a4e31fdd835b7ed7ad2c6189260ee7dbb92dfcaf5d48dbf64d05f65bbc84ac3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T16:16:58Z","title_canon_sha256":"8147389744b700c9b43ea39cedd3ae6c3ff29bd1af5c9da3f8b2f5aa26076c02"},"schema_version":"1.0","source":{"id":"1406.5448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5448","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5448v1","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5448","created_at":"2026-05-18T02:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"7VUAK2IUBLQI","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7VUAK2IUBLQINFDR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7VUAK2IU","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:77e6e5acc8e4deda79b5d0776466b5f046ff902b10af6ef6c686d9fa4cf71a5e","target":"graph","created_at":"2026-05-18T02:49:19Z","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 problem of entire solutions for a class of fourth order, dilation invariant, semilinear elliptic equations with power-type weights and with subcritical or critical growth in the nonlinear term. These equations define non compact variational problems and are characterized by the presence of a term containing lower order derivatives, whose strength is ruled by a parameter {\\lambda}. We can prove existence of entire solutions found as extremal functions for some Rellich-Sobolev type inequalities. Moreover, when the nonlinearity is suitably close to the critical one and the para","authors_text":"Gabriele Cora, Paolo Caldiroli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T16:16:58Z","title":"Entire solutions for a class of fourth order semilinear elliptic equations with weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5448","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:faaf25e7c4a0fd29f74e60364de545952310d86cca343589bccbf94ffb767e62","target":"record","created_at":"2026-05-18T02:49:19Z","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":"a4e31fdd835b7ed7ad2c6189260ee7dbb92dfcaf5d48dbf64d05f65bbc84ac3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-20T16:16:58Z","title_canon_sha256":"8147389744b700c9b43ea39cedd3ae6c3ff29bd1af5c9da3f8b2f5aa26076c02"},"schema_version":"1.0","source":{"id":"1406.5448","kind":"arxiv","version":1}},"canonical_sha256":"fd680569140ae086947107218ecc0fa03dab7fbe1ff7c43b804974529e846558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd680569140ae086947107218ecc0fa03dab7fbe1ff7c43b804974529e846558","first_computed_at":"2026-05-18T02:49:19.073698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:19.073698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNr80GPq5BotV3VKBDBts/VnrG9kxJY6/nMw/XhFXLNlwQdKJQhfULvEVLvMfymW6Mkeb1TAIiTn3jLNfXnxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:19.074206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faaf25e7c4a0fd29f74e60364de545952310d86cca343589bccbf94ffb767e62","sha256:77e6e5acc8e4deda79b5d0776466b5f046ff902b10af6ef6c686d9fa4cf71a5e"],"state_sha256":"e0bcf11f933749f03e26b130d372e20da35f559d95cf0cea3848c3df0b3294ef"}