{"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"}