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We prove that every eigenvalue of the Laplacian operator $-\\Delta$ with the Dirichlet boundary is a concentration value of the Brezis-Nirenberg problem in dimensions $N=4$ and $N=5$ by constructing bubbling solutions with precisely asymptotic profiles via the Ljapunov-Schmidt reduction arguments."},"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":"2503.09250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-03-12T10:46:06Z","cross_cats_sorted":[],"title_canon_sha256":"78c155e1cbf7b4caa04c7516385f9cbca6c13223537be906e331eac352e39828","abstract_canon_sha256":"8b3d79efa550a9692308d5a6d693f25306be1194ee5a6820c7aa11245658e066"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:29:52.651630Z","signature_b64":"SYVwsvCFmZDnjoLQV2LF6O6GXdL4gRkGOahPf9lKU4F9DoyQYJhX2022NBs1mZWjPlgBfjP/xzRB2LQ/Ie/0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e136c89d493737752b3777c336892c20c90a5f593cf4ce0da09f19bb4e01de7","last_reissued_at":"2026-07-05T10:29:52.651144Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:29:52.651144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of bubbling solutions of the Brezis-Nirenberg problem in general bounded domains (I): the dimensions 4 and 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengliu Li, Giusi Vaira, Juncheng Wei, Yuanze Wu","submitted_at":"2025-03-12T10:46:06Z","abstract_excerpt":"In this paper, we consider the Brezis-Nirenberg problem $$ -\\Delta u=\\lambda u+|u|^{\\frac{4}{N-2}}u,\\quad\\mbox{in}\\,\\, \\Omega,\\quad u=0,\\quad\\mbox{on}\\,\\, \\partial\\Omega, $$ where $\\lambda\\in\\mathbb{R}$, $\\Omega\\subset\\mathbb R^N$ is a bounded domain with smooth boundary $\\partial\\Omega$ and $N\\geq3$. We prove that every eigenvalue of the Laplacian operator $-\\Delta$ with the Dirichlet boundary is a concentration value of the Brezis-Nirenberg problem in dimensions $N=4$ and $N=5$ by constructing bubbling solutions with precisely asymptotic profiles via the Ljapunov-Schmidt reduction arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.09250","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.09250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2503.09250","created_at":"2026-07-05T10:29:52.651202+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.09250v1","created_at":"2026-07-05T10:29:52.651202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.09250","created_at":"2026-07-05T10:29:52.651202+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYJWZCOUSNZX","created_at":"2026-07-05T10:29:52.651202+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYJWZCOUSNZXOUVT","created_at":"2026-07-05T10:29:52.651202+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYJWZCOU","created_at":"2026-07-05T10:29:52.651202+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.07602","citing_title":"Sharp quantitative stability estimates for the Brezis-Nirenberg problem","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI","json":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI.json","graph_json":"https://pith.science/api/pith-number/LYJWZCOUSNZXOUVTO56DG2ESYI/graph.json","events_json":"https://pith.science/api/pith-number/LYJWZCOUSNZXOUVTO56DG2ESYI/events.json","paper":"https://pith.science/paper/LYJWZCOU"},"agent_actions":{"view_html":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI","download_json":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI.json","view_paper":"https://pith.science/paper/LYJWZCOU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.09250&json=true","fetch_graph":"https://pith.science/api/pith-number/LYJWZCOUSNZXOUVTO56DG2ESYI/graph.json","fetch_events":"https://pith.science/api/pith-number/LYJWZCOUSNZXOUVTO56DG2ESYI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI/action/storage_attestation","attest_author":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI/action/author_attestation","sign_citation":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI/action/citation_signature","submit_replication":"https://pith.science/pith/LYJWZCOUSNZXOUVTO56DG2ESYI/action/replication_record"}},"created_at":"2026-07-05T10:29:52.651202+00:00","updated_at":"2026-07-05T10:29:52.651202+00:00"}