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In this paper we prove that, if $\\Omega$ is symmetric and $N=4,5$, there exists a sign-changing solution whose positive part concentrates and blows-up at the center of symmetry of the domain, while the negative part vanishes, as $\\lambda\\rightarrow \\lambda_1$, where $\\lambda_1=\\lambda_1(\\Omega)$ denotes the first eigenvalue of $-\\Delta$ o"},"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":"1504.05010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-20T10:53:45Z","cross_cats_sorted":[],"title_canon_sha256":"478ad9b4dd27bafad581536b552a117c9b943079bbec47cb5dd7bc9d634a8ea9","abstract_canon_sha256":"8296fb918699be9f9a92ef466aa5d845f974d5f7a3cc92180c6f822301f69514"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:22.910560Z","signature_b64":"tLM+RBm/Ahb4x0yP0WYrd5CD5Fc8m40xIjaSA3I2xDPimR5MRF+dONlR1sIrkopIjw6feBagfI5bBWUN7WqoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93839ce0d201177634c13937484de53a4704fcc6813c99744e5893555292544e","last_reissued_at":"2026-05-18T02:18:22.909802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:22.909802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign-changing blowing-up solutions for the Brezis--Nirenberg problem in dimensions four and five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Giusi Vaira","submitted_at":"2015-04-20T10:53:45Z","abstract_excerpt":"We consider the Brezis-Nirenberg problem: $$-\\Delta u =\\lambda u + |u|^{p-1}u\\qquad \\mbox{in}\\,\\, \\Omega,\\quad u=0\\,\\, \\mbox{on}\\,\\,\\ \\partial\\Omega,$$ where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$, $N\\geq 3$, $p=\\frac{N+2}{N-2}$ and $\\lambda>0$. 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