{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U7DIYCI3ZIIZVHPU4YW3SNHNUZ","short_pith_number":"pith:U7DIYCI3","canonical_record":{"source":{"id":"1808.08805","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T12:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"542b64dd1ee67d69f55567324c32c3b078b3b2d0949a890069709daae6162b54","abstract_canon_sha256":"d63c9890147df6360c465ecefdfb4aa293095fd5b6d3d7ce2d18a61f57ee5db1"},"schema_version":"1.0"},"canonical_sha256":"a7c68c091bca119a9df4e62db934eda6520d2165cceb25d13e24afadf121d26b","source":{"kind":"arxiv","id":"1808.08805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08805","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08805v1","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08805","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"U7DIYCI3ZIIZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U7DIYCI3ZIIZVHPU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U7DIYCI3","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U7DIYCI3ZIIZVHPU4YW3SNHNUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08805","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T12:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"542b64dd1ee67d69f55567324c32c3b078b3b2d0949a890069709daae6162b54","abstract_canon_sha256":"d63c9890147df6360c465ecefdfb4aa293095fd5b6d3d7ce2d18a61f57ee5db1"},"schema_version":"1.0"},"canonical_sha256":"a7c68c091bca119a9df4e62db934eda6520d2165cceb25d13e24afadf121d26b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:13.188635Z","signature_b64":"iV1qoz5Fc8VrkY4zDpnicsqKMTwiym5k65YtaOFLxKnegM2g+UVp6VusHaC625gVfxq0EWRMYDTqH4jQku0zBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c68c091bca119a9df4e62db934eda6520d2165cceb25d13e24afadf121d26b","last_reissued_at":"2026-05-18T00:07:13.187908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:13.187908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08805","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1xiwqtdhSYp+PM9r6pK3HfUqz0qwNNLhuKoznJrTaPRUGIzy6i9QfyPPmb/8e9U2d6btNm/wjY0gPOBTuNXcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:33.623332Z"},"content_sha256":"097c901426ccd80d2fcab6915433d92e98a56746d3a1ae0a4b9e755092a5439d","schema_version":"1.0","event_id":"sha256:097c901426ccd80d2fcab6915433d92e98a56746d3a1ae0a4b9e755092a5439d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U7DIYCI3ZIIZVHPU4YW3SNHNUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive solutions of quasilinear elliptic equations with exponential nonlinearity combined with convection term","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anderson Luis Albuquerque de Araujo, Luiz Fernando de Oliveira Faria","submitted_at":"2018-08-27T12:03:51Z","abstract_excerpt":"We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension $N$ involving the $N$-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term. In such case, variational methods cannot be applied. Our approach is based on approximation scheme, where we consider a new class of normed spaces of finite dimension. As a particular case, we extended the result achieved by De Araujo and Montenegro [2016] for any $N>2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08805","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mIh1Ttb2QHlMc66TBEu+lt1FUVzz2RifrzCDqOTGOPbNXQMFKdxadEx+0UuNspzjuZnXtLPtc9vPwSjGdLF2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:32:33.624079Z"},"content_sha256":"066c4f30bf94a7abaf28fb9965ef58ba5a17def410ec3a37a2583860939350cf","schema_version":"1.0","event_id":"sha256:066c4f30bf94a7abaf28fb9965ef58ba5a17def410ec3a37a2583860939350cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/bundle.json","state_url":"https://pith.science/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T17:32:33Z","links":{"resolver":"https://pith.science/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ","bundle":"https://pith.science/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/bundle.json","state":"https://pith.science/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7DIYCI3ZIIZVHPU4YW3SNHNUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U7DIYCI3ZIIZVHPU4YW3SNHNUZ","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":"d63c9890147df6360c465ecefdfb4aa293095fd5b6d3d7ce2d18a61f57ee5db1","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T12:03:51Z","title_canon_sha256":"542b64dd1ee67d69f55567324c32c3b078b3b2d0949a890069709daae6162b54"},"schema_version":"1.0","source":{"id":"1808.08805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08805","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08805v1","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08805","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"U7DIYCI3ZIIZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U7DIYCI3ZIIZVHPU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U7DIYCI3","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:066c4f30bf94a7abaf28fb9965ef58ba5a17def410ec3a37a2583860939350cf","target":"graph","created_at":"2026-05-18T00:07:13Z","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 establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension $N$ involving the $N$-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term. In such case, variational methods cannot be applied. Our approach is based on approximation scheme, where we consider a new class of normed spaces of finite dimension. As a particular case, we extended the result achieved by De Araujo and Montenegro [2016] for any $N>2$.","authors_text":"Anderson Luis Albuquerque de Araujo, Luiz Fernando de Oliveira Faria","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T12:03:51Z","title":"Positive solutions of quasilinear elliptic equations with exponential nonlinearity combined with convection term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08805","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":"sha256:097c901426ccd80d2fcab6915433d92e98a56746d3a1ae0a4b9e755092a5439d","target":"record","created_at":"2026-05-18T00:07:13Z","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":"d63c9890147df6360c465ecefdfb4aa293095fd5b6d3d7ce2d18a61f57ee5db1","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T12:03:51Z","title_canon_sha256":"542b64dd1ee67d69f55567324c32c3b078b3b2d0949a890069709daae6162b54"},"schema_version":"1.0","source":{"id":"1808.08805","kind":"arxiv","version":1}},"canonical_sha256":"a7c68c091bca119a9df4e62db934eda6520d2165cceb25d13e24afadf121d26b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c68c091bca119a9df4e62db934eda6520d2165cceb25d13e24afadf121d26b","first_computed_at":"2026-05-18T00:07:13.187908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:13.187908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iV1qoz5Fc8VrkY4zDpnicsqKMTwiym5k65YtaOFLxKnegM2g+UVp6VusHaC625gVfxq0EWRMYDTqH4jQku0zBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:13.188635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:097c901426ccd80d2fcab6915433d92e98a56746d3a1ae0a4b9e755092a5439d","sha256:066c4f30bf94a7abaf28fb9965ef58ba5a17def410ec3a37a2583860939350cf"],"state_sha256":"1ee5d8711d3d891c39d7fed040d15eda813730a521fdfcaf15de27f7e4431d56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFH4scajrnsoBV2ys+fOEWJwihD3MXCtx5VFZ8ARfc5NxSozqjTwkoF+7g4Hh0SyYVGfZ94sL5MSMMHfmqqMDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:32:33.627805Z","bundle_sha256":"86bf867861710109feaa58bdd5533eb7771cec0ed38296faa7e8c6607c7e8a8e"}}