{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VJERQ42JW63VVWTS43JVEEDSJS","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":"9405eb19b2bc2788d4ea90387268e7b3b860f6a114edeba32c4d97035989a618","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-03T17:33:29Z","title_canon_sha256":"cefaf00866e2a2054616384062879bd190f18de356e9e2711341d46e4c0135d6"},"schema_version":"1.0","source":{"id":"1603.01193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01193","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01193v1","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01193","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"VJERQ42JW63V","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VJERQ42JW63VVWTS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VJERQ42J","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ca576eb0d510990656fc520176435abb180c3ce522edcd9fcc7b2cf67a229757","target":"graph","created_at":"2026-05-18T01:19:39Z","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":"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","authors_text":"Carlos Alberto Santos, Jiazheng Zhou","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-03T17:33:29Z","title":"Infinite many Blow-up solutions for a Schr\\\"odinger quasilinear elliptic problem with a non-square diffusion term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01193","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":"sha256:7f24d8ef806cc60722412a966016925f0343caf7a9b7d2691da628f3ead7e609","target":"record","created_at":"2026-05-18T01:19:39Z","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":"9405eb19b2bc2788d4ea90387268e7b3b860f6a114edeba32c4d97035989a618","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-03T17:33:29Z","title_canon_sha256":"cefaf00866e2a2054616384062879bd190f18de356e9e2711341d46e4c0135d6"},"schema_version":"1.0","source":{"id":"1603.01193","kind":"arxiv","version":1}},"canonical_sha256":"aa49187349b7b75ada72e6d35210724c913f4c0fea0b2f443a9359d619b476a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa49187349b7b75ada72e6d35210724c913f4c0fea0b2f443a9359d619b476a5","first_computed_at":"2026-05-18T01:19:39.442171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:39.442171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pUkFjbZsq15s75C3VjQggYOErow/mADklWLkg/srWm7FQvjV3YPa8TQGD68VSpSmf3umfhSNr+T95ipJE9P8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:39.442924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f24d8ef806cc60722412a966016925f0343caf7a9b7d2691da628f3ead7e609","sha256:ca576eb0d510990656fc520176435abb180c3ce522edcd9fcc7b2cf67a229757"],"state_sha256":"4e5c0915cf5cda0d65b124802e436b0939a6e4367850a6fb60ee7371c0347841"}