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More precisely, for a given positive integer $K$, we derive asymptotic $C^1$-expansions for the negative eigenvalues of the linearization of the unique radial solution $u_\\alpha$ of $(H)$ "},"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":"1901.00453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-02T17:32:31Z","cross_cats_sorted":[],"title_canon_sha256":"6b4e6dc8b13a438d8559aa74cd0d42798b2f3fca8b3678b05b4f0fa0ac94cb87","abstract_canon_sha256":"9462d16a2bfb087f9c0783b0605753a050ff853a9c4c5f43c77eb9dec71cf6a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:03.812389Z","signature_b64":"/AtdvHdWO8dHyF6ZRj2you0/yVFwMWHTxmuefIXeDGe0jwxk7DOLCIyC8Q33oAeoV19w3XCvsm4zhJwFhNc6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"017571aa46b0383db62f4222eec01e6223c29fcc7b274e14ca9490b3352a9db1","last_reissued_at":"2026-05-17T23:57:03.811755Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:03.811755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral asymptotics of radial solutions and nonradial bifurcation for the H\\'enon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joel K\\\"ubler, Tobias Weth","submitted_at":"2019-01-02T17:32:31Z","abstract_excerpt":"We study the spectral asymptotics of nodal (i.e., sign-changing) solutions of the problem\n  \\begin{equation*} (H) \\qquad \\qquad \\left \\{\n  \\begin{aligned}\n  -\\Delta u &=|x|^\\alpha |u|^{p-2}u&&\\qquad \\text{in ${\\bf B}$,} \\\\\n  u&=0&&\\qquad \\text{on $\\partial {\\bf B}$,}\n  \\end{aligned}\n  \\right.\n  \\end{equation*}\n  in the unit ball ${\\bf B} \\subset \\mathbb{R}^N,N\\geq 3$, $p>2$ in the limit $\\alpha \\to +\\infty$. More precisely, for a given positive integer $K$, we derive asymptotic $C^1$-expansions for the negative eigenvalues of the linearization of the unique radial solution $u_\\alpha$ of $(H)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00453","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":"1901.00453","created_at":"2026-05-17T23:57:03.811851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.00453v1","created_at":"2026-05-17T23:57:03.811851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00453","created_at":"2026-05-17T23:57:03.811851+00:00"},{"alias_kind":"pith_short_12","alias_value":"AF2XDKSGWA4D","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"AF2XDKSGWA4D3NRP","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"AF2XDKSG","created_at":"2026-05-18T12:33:12.712433+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/AF2XDKSGWA4D3NRPIIRO5QA6MI","json":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI.json","graph_json":"https://pith.science/api/pith-number/AF2XDKSGWA4D3NRPIIRO5QA6MI/graph.json","events_json":"https://pith.science/api/pith-number/AF2XDKSGWA4D3NRPIIRO5QA6MI/events.json","paper":"https://pith.science/paper/AF2XDKSG"},"agent_actions":{"view_html":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI","download_json":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI.json","view_paper":"https://pith.science/paper/AF2XDKSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.00453&json=true","fetch_graph":"https://pith.science/api/pith-number/AF2XDKSGWA4D3NRPIIRO5QA6MI/graph.json","fetch_events":"https://pith.science/api/pith-number/AF2XDKSGWA4D3NRPIIRO5QA6MI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI/action/storage_attestation","attest_author":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI/action/author_attestation","sign_citation":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI/action/citation_signature","submit_replication":"https://pith.science/pith/AF2XDKSGWA4D3NRPIIRO5QA6MI/action/replication_record"}},"created_at":"2026-05-17T23:57:03.811851+00:00","updated_at":"2026-05-17T23:57:03.811851+00:00"}