{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YIQFPOEBXHMEYUH655RENPX347","short_pith_number":"pith:YIQFPOEB","schema_version":"1.0","canonical_sha256":"c22057b881b9d84c50feef6246befbe7ddf3c2713c3f51a6453e7f931953ba9d","source":{"kind":"arxiv","id":"1109.4550","version":1},"attestation_state":"computed","paper":{"title":"Entire solutions to nonlinear scalar field equations with indefinite linear part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gilles \\'Ev\\'equoz, Tobias Weth","submitted_at":"2011-09-21T14:55:38Z","abstract_excerpt":"We consider the stationary semilinear Schr\\\"odinger equation $-\\Delta u + a(x) u = f(x,u)$, $u\\in H^1(\\R^N)$, where $a$ and $f$ are continuous functions converging to some limits $a_\\infty>0$ and $f_\\infty=f_\\infty(u)$ as $|x|\\to\\infty$. In the indefinite setting where the Schr\\\"odinger operator $-\\Delta +a$ has negative eigenvalues, we combine a reduction method with a topological argument to prove the existence of a solution of our problem under weak one-sided asymptotic estimates. The minimal energy level need not be attained in this case. In a second part of the paper, we prove the existen"},"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":"1109.4550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-21T14:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"971bc3d50c49cfa5a26273e4ba9abaa421bdefde93d2698d9bb170d27c713080","abstract_canon_sha256":"e56b3aaefa2e84ae81c1999bcd90f8d888c03058001fd8384b76588d87b05a91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:34.474107Z","signature_b64":"MLOQ2iakVx4ZnLxqMyc0dERHbSNWslJFHp5W8DkNeVlWKHU3vQt99lzv6jXEO8RDqkabwp1nmTTVMYsz8+0qCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c22057b881b9d84c50feef6246befbe7ddf3c2713c3f51a6453e7f931953ba9d","last_reissued_at":"2026-05-18T04:12:34.473458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:34.473458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entire solutions to nonlinear scalar field equations with indefinite linear part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gilles \\'Ev\\'equoz, Tobias Weth","submitted_at":"2011-09-21T14:55:38Z","abstract_excerpt":"We consider the stationary semilinear Schr\\\"odinger equation $-\\Delta u + a(x) u = f(x,u)$, $u\\in H^1(\\R^N)$, where $a$ and $f$ are continuous functions converging to some limits $a_\\infty>0$ and $f_\\infty=f_\\infty(u)$ as $|x|\\to\\infty$. In the indefinite setting where the Schr\\\"odinger operator $-\\Delta +a$ has negative eigenvalues, we combine a reduction method with a topological argument to prove the existence of a solution of our problem under weak one-sided asymptotic estimates. The minimal energy level need not be attained in this case. In a second part of the paper, we prove the existen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4550","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":"1109.4550","created_at":"2026-05-18T04:12:34.473562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4550v1","created_at":"2026-05-18T04:12:34.473562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4550","created_at":"2026-05-18T04:12:34.473562+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIQFPOEBXHME","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIQFPOEBXHMEYUH6","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIQFPOEB","created_at":"2026-05-18T12:26:47.523578+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/YIQFPOEBXHMEYUH655RENPX347","json":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347.json","graph_json":"https://pith.science/api/pith-number/YIQFPOEBXHMEYUH655RENPX347/graph.json","events_json":"https://pith.science/api/pith-number/YIQFPOEBXHMEYUH655RENPX347/events.json","paper":"https://pith.science/paper/YIQFPOEB"},"agent_actions":{"view_html":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347","download_json":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347.json","view_paper":"https://pith.science/paper/YIQFPOEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4550&json=true","fetch_graph":"https://pith.science/api/pith-number/YIQFPOEBXHMEYUH655RENPX347/graph.json","fetch_events":"https://pith.science/api/pith-number/YIQFPOEBXHMEYUH655RENPX347/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347/action/storage_attestation","attest_author":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347/action/author_attestation","sign_citation":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347/action/citation_signature","submit_replication":"https://pith.science/pith/YIQFPOEBXHMEYUH655RENPX347/action/replication_record"}},"created_at":"2026-05-18T04:12:34.473562+00:00","updated_at":"2026-05-18T04:12:34.473562+00:00"}