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We use the inversion $u\\to v:= u/\\Vert u\\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables $(\\lambda,v) \\in "},"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":"1106.5879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-29T08:58:17Z","cross_cats_sorted":[],"title_canon_sha256":"a34a8d980dfa5220d1e8a1749f731f9bb9ebe69b58cf48981930a077bd6ac992","abstract_canon_sha256":"69735e137272024427aefe8c8d565d70a9e10c07ef3054e6ac20c9da92549ff9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:42.071101Z","signature_b64":"GLphrRcy2ji+tUsS3m5PwBhTniQBe8dzHr7hrCSQOKWpRQu67ztiOHTn8XP96uVaYF+2PS5/arV2arx2QZY8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d747ee6295fe4c8a61900d8bd1d5041f5272b0f241237c2e22e2e5f686fbf74","last_reissued_at":"2026-05-18T03:24:42.070493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:42.070493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global bifurcation for asymptotically linear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Genoud","submitted_at":"2011-06-29T08:58:17Z","abstract_excerpt":"We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\\\"odinger equations \\begin{equation}\\label{1} \\{{array}{lr} \\D u + f(x,u)u = \\lam u \\quad \\text{in} \\ {\\mathbb R}^N, u \\in H^1({\\mathbb R}^N)\\setmimus\\{0\\}, \\quad N \\ge 1. {array}. \\end{equation} The method is topological, based on recent developments of degree theory. We use the inversion $u\\to v:= u/\\Vert u\\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables $(\\lambda,v) \\in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5879","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":"1106.5879","created_at":"2026-05-18T03:24:42.070619+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5879v1","created_at":"2026-05-18T03:24:42.070619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5879","created_at":"2026-05-18T03:24:42.070619+00:00"},{"alias_kind":"pith_short_12","alias_value":"DV2H5ZRJL7SM","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DV2H5ZRJL7SMRJQZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DV2H5ZRJ","created_at":"2026-05-18T12:26:26.731475+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/DV2H5ZRJL7SMRJQZADML2HKQIH","json":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH.json","graph_json":"https://pith.science/api/pith-number/DV2H5ZRJL7SMRJQZADML2HKQIH/graph.json","events_json":"https://pith.science/api/pith-number/DV2H5ZRJL7SMRJQZADML2HKQIH/events.json","paper":"https://pith.science/paper/DV2H5ZRJ"},"agent_actions":{"view_html":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH","download_json":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH.json","view_paper":"https://pith.science/paper/DV2H5ZRJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5879&json=true","fetch_graph":"https://pith.science/api/pith-number/DV2H5ZRJL7SMRJQZADML2HKQIH/graph.json","fetch_events":"https://pith.science/api/pith-number/DV2H5ZRJL7SMRJQZADML2HKQIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH/action/storage_attestation","attest_author":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH/action/author_attestation","sign_citation":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH/action/citation_signature","submit_replication":"https://pith.science/pith/DV2H5ZRJL7SMRJQZADML2HKQIH/action/replication_record"}},"created_at":"2026-05-18T03:24:42.070619+00:00","updated_at":"2026-05-18T03:24:42.070619+00:00"}