{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VJERQ42JW63VVWTS43JVEEDSJS","short_pith_number":"pith:VJERQ42J","schema_version":"1.0","canonical_sha256":"aa49187349b7b75ada72e6d35210724c913f4c0fea0b2f443a9359d619b476a5","source":{"kind":"arxiv","id":"1603.01193","version":1},"attestation_state":"computed","paper":{"title":"Infinite many Blow-up solutions for a Schr\\\"odinger quasilinear elliptic problem with a non-square diffusion term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Carlos Alberto Santos, Jiazheng Zhou","submitted_at":"2016-03-03T17:33:29Z","abstract_excerpt":"In this paper, we consider existence of positive solutions for the Schr\\\"odinger quasilinear elliptic problem $$\n  \\left\\{ \\begin{array}{l} \\Delta_pu+\\Delta_p(|u|^{2\\gamma})|u|^{2\\gamma-2}u = a(x)g(u)~ \\mbox{on}~ \\mathbb{R}^N,\\\\ u>0\\ \\mbox{in}~\\mathbb{R}^N,\\ u(x)\\stackrel{\\left|x\\right|\\rightarrow \\infty}{\\longrightarrow} \\infty, \\end{array} \\right. $$ where $a(x), ~x\\in \\mathbb{R}^N$ and $g(s)~s>0$ are a nonnegative and continuous functions with $g$ being nonincreasing as well, $\\gamma>{1}/{2}$, and $N \\geq 1$. By a dual approach we establish sufficient conditions for existence and multiplici"},"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":"1603.01193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-03T17:33:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cefaf00866e2a2054616384062879bd190f18de356e9e2711341d46e4c0135d6","abstract_canon_sha256":"9405eb19b2bc2788d4ea90387268e7b3b860f6a114edeba32c4d97035989a618"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:39.442924Z","signature_b64":"pUkFjbZsq15s75C3VjQggYOErow/mADklWLkg/srWm7FQvjV3YPa8TQGD68VSpSmf3umfhSNr+T95ipJE9P8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa49187349b7b75ada72e6d35210724c913f4c0fea0b2f443a9359d619b476a5","last_reissued_at":"2026-05-18T01:19:39.442171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:39.442171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite many Blow-up solutions for a Schr\\\"odinger quasilinear elliptic problem with a non-square diffusion term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Carlos Alberto Santos, Jiazheng Zhou","submitted_at":"2016-03-03T17:33:29Z","abstract_excerpt":"In this paper, we consider existence of positive solutions for the Schr\\\"odinger quasilinear elliptic problem $$\n  \\left\\{ \\begin{array}{l} \\Delta_pu+\\Delta_p(|u|^{2\\gamma})|u|^{2\\gamma-2}u = a(x)g(u)~ \\mbox{on}~ \\mathbb{R}^N,\\\\ u>0\\ \\mbox{in}~\\mathbb{R}^N,\\ u(x)\\stackrel{\\left|x\\right|\\rightarrow \\infty}{\\longrightarrow} \\infty, \\end{array} \\right. $$ where $a(x), ~x\\in \\mathbb{R}^N$ and $g(s)~s>0$ are a nonnegative and continuous functions with $g$ being nonincreasing as well, $\\gamma>{1}/{2}$, and $N \\geq 1$. By a dual approach we establish sufficient conditions for existence and multiplici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01193","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":"1603.01193","created_at":"2026-05-18T01:19:39.442300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01193v1","created_at":"2026-05-18T01:19:39.442300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01193","created_at":"2026-05-18T01:19:39.442300+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJERQ42JW63V","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJERQ42JW63VVWTS","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJERQ42J","created_at":"2026-05-18T12:30:48.956258+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/VJERQ42JW63VVWTS43JVEEDSJS","json":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS.json","graph_json":"https://pith.science/api/pith-number/VJERQ42JW63VVWTS43JVEEDSJS/graph.json","events_json":"https://pith.science/api/pith-number/VJERQ42JW63VVWTS43JVEEDSJS/events.json","paper":"https://pith.science/paper/VJERQ42J"},"agent_actions":{"view_html":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS","download_json":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS.json","view_paper":"https://pith.science/paper/VJERQ42J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01193&json=true","fetch_graph":"https://pith.science/api/pith-number/VJERQ42JW63VVWTS43JVEEDSJS/graph.json","fetch_events":"https://pith.science/api/pith-number/VJERQ42JW63VVWTS43JVEEDSJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS/action/storage_attestation","attest_author":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS/action/author_attestation","sign_citation":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS/action/citation_signature","submit_replication":"https://pith.science/pith/VJERQ42JW63VVWTS43JVEEDSJS/action/replication_record"}},"created_at":"2026-05-18T01:19:39.442300+00:00","updated_at":"2026-05-18T01:19:39.442300+00:00"}