{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZRY76IKH7NPDPSZD56IQFNLBLP","short_pith_number":"pith:ZRY76IKH","canonical_record":{"source":{"id":"1704.03562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-11T22:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"c389a7ce0fe1420def44085895650d26632d30e3a27dd389b927f628cf4092bf","abstract_canon_sha256":"57f2308a0feb1a9f1189e1a49cda03ca827cdaa9930c4b04b17324906a2d8220"},"schema_version":"1.0"},"canonical_sha256":"cc71ff2147fb5e37cb23ef9102b5615be307cd373bf8e441db1aff6651ef9516","source":{"kind":"arxiv","id":"1704.03562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03562","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03562v2","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03562","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZRY76IKH7NPD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZRY76IKH7NPDPSZD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZRY76IKH","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZRY76IKH7NPDPSZD56IQFNLBLP","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-11T22:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"c389a7ce0fe1420def44085895650d26632d30e3a27dd389b927f628cf4092bf","abstract_canon_sha256":"57f2308a0feb1a9f1189e1a49cda03ca827cdaa9930c4b04b17324906a2d8220"},"schema_version":"1.0"},"canonical_sha256":"cc71ff2147fb5e37cb23ef9102b5615be307cd373bf8e441db1aff6651ef9516","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:34.802837Z","signature_b64":"/X+uRAlxofw5FfJ6idMBhLnK6xpR5rYstv3Pk9pDVZsX8iLuoBFowHoCc75P5z0h1nmrfPzp2vAe9AWb2XUBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc71ff2147fb5e37cb23ef9102b5615be307cd373bf8e441db1aff6651ef9516","last_reissued_at":"2026-05-18T00:40:34.802072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:34.802072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03562","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppcsfGc88Nu1nfyCKMJipEdqD7zjP3114Yc43mMKtR7Vj1uB2MntcnFEfWlBWprwThsDXqJ2xKz8DZ42v9z5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:42:28.382105Z"},"content_sha256":"16b83d8ef68e283b36f603549da285b571c3612903b80b6f740c9919253a3f1a","schema_version":"1.0","event_id":"sha256:16b83d8ef68e283b36f603549da285b571c3612903b80b6f740c9919253a3f1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZRY76IKH7NPDPSZD56IQFNLBLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of solution for a class of quasilinear problem in Orlicz-Sobolev space without $\\Delta_2$-condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Edcarlos D. Silva, Marcos T. O. Pimenta","submitted_at":"2017-04-11T22:52:02Z","abstract_excerpt":"\\noindent In this paper we study existence of solution for a class of problem of the type $$ \\left\\{ \\begin{array}{ll} -\\Delta_{\\Phi}{u}=f(u), \\quad \\mbox{in} \\quad \\Omega u=0, \\quad \\mbox{on} \\quad \\partial \\Omega, \\end{array} \\right. $$ where $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, is a smooth bounded domain, $f:\\mathbb{R} \\to \\mathbb{R}$ is a continuous function verifying some conditions, and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ is a N-function which is not assumed to satisfy the well known $\\Delta_2$-condition, then the Orlicz-Sobolev space $W^{1,\\Phi}_0(\\Omega)$ can be non reflexive. As ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03562","kind":"arxiv","version":2},"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":"2026-05-18T00:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YKX7Ld7t0W2L9xHvepOfXO2XKkSy9djxcXoEjorPAZXmdL0OcyUnkbkrPMFolj8xJVR2/nrKnRa8/vdz1yVMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:42:28.382709Z"},"content_sha256":"54100db5c7c273ef42d049c10252354e292a5f9ae74993f07a5fa622b18c35d1","schema_version":"1.0","event_id":"sha256:54100db5c7c273ef42d049c10252354e292a5f9ae74993f07a5fa622b18c35d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/bundle.json","state_url":"https://pith.science/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/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":"2026-05-31T15:42:28Z","links":{"resolver":"https://pith.science/pith/ZRY76IKH7NPDPSZD56IQFNLBLP","bundle":"https://pith.science/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/bundle.json","state":"https://pith.science/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRY76IKH7NPDPSZD56IQFNLBLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZRY76IKH7NPDPSZD56IQFNLBLP","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":"57f2308a0feb1a9f1189e1a49cda03ca827cdaa9930c4b04b17324906a2d8220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-11T22:52:02Z","title_canon_sha256":"c389a7ce0fe1420def44085895650d26632d30e3a27dd389b927f628cf4092bf"},"schema_version":"1.0","source":{"id":"1704.03562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03562","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03562v2","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03562","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZRY76IKH7NPD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZRY76IKH7NPDPSZD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZRY76IKH","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:54100db5c7c273ef42d049c10252354e292a5f9ae74993f07a5fa622b18c35d1","target":"graph","created_at":"2026-05-18T00:40:34Z","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":"\\noindent In this paper we study existence of solution for a class of problem of the type $$ \\left\\{ \\begin{array}{ll} -\\Delta_{\\Phi}{u}=f(u), \\quad \\mbox{in} \\quad \\Omega u=0, \\quad \\mbox{on} \\quad \\partial \\Omega, \\end{array} \\right. $$ where $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, is a smooth bounded domain, $f:\\mathbb{R} \\to \\mathbb{R}$ is a continuous function verifying some conditions, and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ is a N-function which is not assumed to satisfy the well known $\\Delta_2$-condition, then the Orlicz-Sobolev space $W^{1,\\Phi}_0(\\Omega)$ can be non reflexive. As ma","authors_text":"Claudianor O. Alves, Edcarlos D. Silva, Marcos T. O. Pimenta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-11T22:52:02Z","title":"Existence of solution for a class of quasilinear problem in Orlicz-Sobolev space without $\\Delta_2$-condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03562","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":"sha256:16b83d8ef68e283b36f603549da285b571c3612903b80b6f740c9919253a3f1a","target":"record","created_at":"2026-05-18T00:40:34Z","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":"57f2308a0feb1a9f1189e1a49cda03ca827cdaa9930c4b04b17324906a2d8220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-11T22:52:02Z","title_canon_sha256":"c389a7ce0fe1420def44085895650d26632d30e3a27dd389b927f628cf4092bf"},"schema_version":"1.0","source":{"id":"1704.03562","kind":"arxiv","version":2}},"canonical_sha256":"cc71ff2147fb5e37cb23ef9102b5615be307cd373bf8e441db1aff6651ef9516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc71ff2147fb5e37cb23ef9102b5615be307cd373bf8e441db1aff6651ef9516","first_computed_at":"2026-05-18T00:40:34.802072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:34.802072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/X+uRAlxofw5FfJ6idMBhLnK6xpR5rYstv3Pk9pDVZsX8iLuoBFowHoCc75P5z0h1nmrfPzp2vAe9AWb2XUBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:34.802837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16b83d8ef68e283b36f603549da285b571c3612903b80b6f740c9919253a3f1a","sha256:54100db5c7c273ef42d049c10252354e292a5f9ae74993f07a5fa622b18c35d1"],"state_sha256":"c40c043ab6bb3c39f6aa4bbf3e44c296f1214e2629a89211bc75242b63f5eeaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cSAPaXkEi978/wPkFpZ+GwTMhnZcsSRyi9DKVg9xRLj+gVhsaBcE9hqQGpFTbJpIkYLYAuJJtE51XVSjZxvvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:42:28.388134Z","bundle_sha256":"622b2e4a9cb8307ec24b9d10baa30129c26eba2a656764dd55ca3a49633ca121"}}