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We give the first example of sign-changing {\\it bubbling} solutions to the nonlinear elliptic problem $$\n  -\\Delta u=|u|^{{n+2\\over n-2} +\\ve -1 } u \\, \\, \\mbox{ in } \\Omega , \\quad \\quad\n  u=0 \\mbox{ on } \\partial \\Omega, $$ where $\\ve$ is a small positive parameter. The basic cell in the construction is the sign-changing nodal solution to the critical Yamabe problem $$ -\\Delta w = |w|^{\\frac{4}{n-2}} w, \\ \\ w \\in {\\mathcal D}^{1,2} (\\R^n) $$ which has large number ($3n$) of kernels."},"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":"1502.01674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-05T18:43:20Z","cross_cats_sorted":[],"title_canon_sha256":"63316a0cbf4e88d62d0d2770e123deb16c199870e24eb48b48b64e7f239d2537","abstract_canon_sha256":"ddf3db32c0c77ce7d60b5c34f44eea5638c7d3154056500d92fc2f32ec870059"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:51.568630Z","signature_b64":"LzVQDPnAf+akhb35sk22pjPHHSLfU+s0Vgsos0hSHhZXeEnOAnLB7E4jEIOZIGvL+twkYz4+hONlnByEVJHDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b54930b141f3a77101a6c5a9ce6e04778b2ab1961366e9b35043e8c3170bf09","last_reissued_at":"2026-05-18T02:27:51.568136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:51.568136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Monica Musso","submitted_at":"2015-02-05T18:43:20Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\R^n$, $n\\ge 3$ with smooth boundary $\\partial\\Omega$ and a small hole. We give the first example of sign-changing {\\it bubbling} solutions to the nonlinear elliptic problem $$\n  -\\Delta u=|u|^{{n+2\\over n-2} +\\ve -1 } u \\, \\, \\mbox{ in } \\Omega , \\quad \\quad\n  u=0 \\mbox{ on } \\partial \\Omega, $$ where $\\ve$ is a small positive parameter. The basic cell in the construction is the sign-changing nodal solution to the critical Yamabe problem $$ -\\Delta w = |w|^{\\frac{4}{n-2}} w, \\ \\ w \\in {\\mathcal D}^{1,2} (\\R^n) $$ which has large number ($3n$) of kernels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01674","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":"1502.01674","created_at":"2026-05-18T02:27:51.568214+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01674v1","created_at":"2026-05-18T02:27:51.568214+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01674","created_at":"2026-05-18T02:27:51.568214+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNKJGCYUD45H","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNKJGCYUD45HOEA2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNKJGCYU","created_at":"2026-05-18T12:29:14.074870+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/BNKJGCYUD45HOEA2NRNJZZXAI5","json":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5.json","graph_json":"https://pith.science/api/pith-number/BNKJGCYUD45HOEA2NRNJZZXAI5/graph.json","events_json":"https://pith.science/api/pith-number/BNKJGCYUD45HOEA2NRNJZZXAI5/events.json","paper":"https://pith.science/paper/BNKJGCYU"},"agent_actions":{"view_html":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5","download_json":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5.json","view_paper":"https://pith.science/paper/BNKJGCYU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01674&json=true","fetch_graph":"https://pith.science/api/pith-number/BNKJGCYUD45HOEA2NRNJZZXAI5/graph.json","fetch_events":"https://pith.science/api/pith-number/BNKJGCYUD45HOEA2NRNJZZXAI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5/action/storage_attestation","attest_author":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5/action/author_attestation","sign_citation":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5/action/citation_signature","submit_replication":"https://pith.science/pith/BNKJGCYUD45HOEA2NRNJZZXAI5/action/replication_record"}},"created_at":"2026-05-18T02:27:51.568214+00:00","updated_at":"2026-05-18T02:27:51.568214+00:00"}