{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J5UPEZHUUBPVDPQEWGAUQBCWDC","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":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53"},"schema_version":"1.0","source":{"id":"1307.6578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6578v2","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"J5UPEZHUUBPV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J5UPEZHUUBPVDPQE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J5UPEZHU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82","target":"graph","created_at":"2026-05-18T02:59:08Z","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 semilinear elliptic equation $\\Delta u + g(x,u,Du) = 0$ in $\\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples.","authors_text":"Lucas C. F. Ferreira, Marcelo Montenegro, Matheus C. Santos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title":"Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6578","kind":"arxiv","version":2},"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:b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06","target":"record","created_at":"2026-05-18T02:59:08Z","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":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53"},"schema_version":"1.0","source":{"id":"1307.6578","kind":"arxiv","version":2}},"canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","first_computed_at":"2026-05-18T02:59:08.636834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:08.636834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38b9D+UKFSkjR4LY2cn6OsRgRoxbzC/GhPAY3CZWJek+iNRPqY9eHuJSvhLHoAYxXzSz1xh19vIz9kNpe/ABBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:08.637422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06","sha256:ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82"],"state_sha256":"2364ee3633e159e56cfc1d773a5acbe41ddc5ea5292b351881eacf33715b90a1"}