{"paper":{"title":"Multiplicity of normalized solutions for a Schr\\\"{o}dinger equation with critical growth in $\\mathbb{R}^{N}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Ji, Claudianor O. Alves, Olimpio H. Miyagaki","submitted_at":"2021-03-14T14:36:52Z","abstract_excerpt":"In this paper we study the multiplicity of normalized solutions to the following nonlinear Schr\\\"{o}dinger equation with critical growth \\begin{align*}\n  \\left\\{ \\begin{aligned} &-\\Delta u=\\lambda u+\\mu |u|^{q-2}u+f(u), \\quad \\quad \\hbox{in }\\mathbb{R}^N,\\\\ &\\int_{\\mathbb{R}^{N}}|u|^{2}dx=a^{2}, \\end{aligned} \\right. \\end{align*} where $a,\\mu>0$, $\\lambda\\in \\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $q \\in (2,2+\\frac{4}{N})$ and $f$ has an exponential critical growth when $N=2$, and $f(u)=|u|^{2^*-2}u$ when $N \\geq 3$ and $2^{*}=\\frac{2N}{N-2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.07940","kind":"arxiv","version":2},"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/2103.07940/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"}