{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2HS5LSKEZ64HPBBEOZGAN7HQ7S","short_pith_number":"pith:2HS5LSKE","schema_version":"1.0","canonical_sha256":"d1e5d5c944cfb8778424764c06fcf0fca4a41740c86c434101b46f0784149fd8","source":{"kind":"arxiv","id":"1506.01669","version":1},"attestation_state":"computed","paper":{"title":"Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ailton R. Silva, Claudianor O. Alves","submitted_at":"2015-06-04T18:04:03Z","abstract_excerpt":"In this paper, we study existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems \\[ - \\Delta_{\\Phi}u + V(\\epsilon x)\\phi(\\vert u\\vert)u = f(u)\\quad \\mbox{in} \\quad \\mathbb{R}^{N} \\,\\,\\, ( N\\geq 2 ), \\] where $\\Phi(t) = \\int_{0}^{\\vert t\\vert}\\phi(s)sds$ is a N-function, $ \\Delta_{\\Phi}$ is the $\\Phi$-Laplacian operator, $\\epsilon$ is a positive parameter, $V : \\mathbb{R}^{N} \\rightarrow \\mathbb{R} $ is a continuous function and $f : \\mathbb{R} \\rightarrow \\mathbb{R} $ is a $C^{1}$-function."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.01669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-04T18:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"a472d57d0cc914cbf4e7cc8ccbaea7ae10793644a1531be9363baa902dd593a6","abstract_canon_sha256":"f66172442b77255bcae123114fb173ee377a9eeb543a53e67dc04177af06cb3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:18.468835Z","signature_b64":"bH409UpVjTI+QqMRic5kSgpZJIY2DwAK9aLBxu6UHbyVRM6b7yZQyeFFonJDcRWBr+zO+UJ5sjpTdGUzwlS+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e5d5c944cfb8778424764c06fcf0fca4a41740c86c434101b46f0784149fd8","last_reissued_at":"2026-05-18T00:57:18.468164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:18.468164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ailton R. Silva, Claudianor O. Alves","submitted_at":"2015-06-04T18:04:03Z","abstract_excerpt":"In this paper, we study existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems \\[ - \\Delta_{\\Phi}u + V(\\epsilon x)\\phi(\\vert u\\vert)u = f(u)\\quad \\mbox{in} \\quad \\mathbb{R}^{N} \\,\\,\\, ( N\\geq 2 ), \\] where $\\Phi(t) = \\int_{0}^{\\vert t\\vert}\\phi(s)sds$ is a N-function, $ \\Delta_{\\Phi}$ is the $\\Phi$-Laplacian operator, $\\epsilon$ is a positive parameter, $V : \\mathbb{R}^{N} \\rightarrow \\mathbb{R} $ is a continuous function and $f : \\mathbb{R} \\rightarrow \\mathbb{R} $ is a $C^{1}$-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01669","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.01669","created_at":"2026-05-18T00:57:18.468265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01669v1","created_at":"2026-05-18T00:57:18.468265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01669","created_at":"2026-05-18T00:57:18.468265+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HS5LSKEZ64H","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HS5LSKEZ64HPBBE","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HS5LSKE","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S","json":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S.json","graph_json":"https://pith.science/api/pith-number/2HS5LSKEZ64HPBBEOZGAN7HQ7S/graph.json","events_json":"https://pith.science/api/pith-number/2HS5LSKEZ64HPBBEOZGAN7HQ7S/events.json","paper":"https://pith.science/paper/2HS5LSKE"},"agent_actions":{"view_html":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S","download_json":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S.json","view_paper":"https://pith.science/paper/2HS5LSKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01669&json=true","fetch_graph":"https://pith.science/api/pith-number/2HS5LSKEZ64HPBBEOZGAN7HQ7S/graph.json","fetch_events":"https://pith.science/api/pith-number/2HS5LSKEZ64HPBBEOZGAN7HQ7S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S/action/storage_attestation","attest_author":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S/action/author_attestation","sign_citation":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S/action/citation_signature","submit_replication":"https://pith.science/pith/2HS5LSKEZ64HPBBEOZGAN7HQ7S/action/replication_record"}},"created_at":"2026-05-18T00:57:18.468265+00:00","updated_at":"2026-05-18T00:57:18.468265+00:00"}