{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CQAH4DQFDM2ZAUU7VMUX4FJI2H","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":"85971af13a61f06595487cdf240cee7f54dbd59e4f84abc319950a1e86c859bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-31T18:03:49Z","title_canon_sha256":"8b957ccdbbdf7c208b69a8ce4331cc25cafe2bef69d1c61e645cc63e455a317e"},"schema_version":"1.0","source":{"id":"1208.6562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6562","created_at":"2026-05-18T03:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6562v1","created_at":"2026-05-18T03:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6562","created_at":"2026-05-18T03:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"CQAH4DQFDM2Z","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CQAH4DQFDM2ZAUU7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CQAH4DQF","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:0b2c645aa9f5827e8a79399b4261f99e5321f105135e054bb0347c036059981a","target":"graph","created_at":"2026-05-18T03:46:32Z","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 solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on $\\Delta u\\pm g(|\\nabla u|)= f(u)$, $u\\ge0$, where $f$ and $g$ are increasing continuous functions. We give conditions on $f$ and $g$ which guarantee the availability or the absence of positive solutions of such equations in $\\R^N$. Our results considerably improve the existing ones and are sharp or close to sharp in the model cases. In particular, we completely characterize the solvability of such equations when $f$ and $g$ have power growth at infinity. We also deri","authors_text":"Alexander Quaas, Boyan Sirakov, Patricio Felmer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-31T18:03:49Z","title":"Solvability of nonlinear elliptic equations with gradient terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6562","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":"sha256:3038856d29a3ea05f20363c2aa3b65b714d489514480855ec68508cf524ebd6c","target":"record","created_at":"2026-05-18T03:46:32Z","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":"85971af13a61f06595487cdf240cee7f54dbd59e4f84abc319950a1e86c859bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-31T18:03:49Z","title_canon_sha256":"8b957ccdbbdf7c208b69a8ce4331cc25cafe2bef69d1c61e645cc63e455a317e"},"schema_version":"1.0","source":{"id":"1208.6562","kind":"arxiv","version":1}},"canonical_sha256":"14007e0e051b3590529fab297e1528d1c34efda54064f49030a98692ffd50730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14007e0e051b3590529fab297e1528d1c34efda54064f49030a98692ffd50730","first_computed_at":"2026-05-18T03:46:32.620192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:32.620192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3JU3I6DpdXR4y3iCTK7vFXRS3JtKpH/Yht2HuUkb7yKKfnPi2Svf//Dp1ebvWip8admUsWCsIrfzdJPm8LQ+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:32.621066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3038856d29a3ea05f20363c2aa3b65b714d489514480855ec68508cf524ebd6c","sha256:0b2c645aa9f5827e8a79399b4261f99e5321f105135e054bb0347c036059981a"],"state_sha256":"b70a98ab2f6edeb971a1e562b5673ea22b66a12b64fb099dbbc4338cc85b588e"}