{"paper":{"title":"Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gongbao LI, Tao Yang, Xiao Luo","submitted_at":"2021-03-15T03:00:53Z","abstract_excerpt":"In this paper, we consider the existence and asymptotic properties of solutions to the following Kirchhoff equation \\begin{equation}\\label{1}\\nonumber - \\Bigl(a+b\\int_{{\\R^3}} {{{\\left| {\\nabla u} \\right|}^2}}\\Bigl) \\Delta u\n  =\\lambda u+ {| u |^{p - 2}}u+\\mu {| u |^{q - 2}}u \\text { in } \\mathbb{R}^{3} \\end{equation} under the normalized constraint $\\int_{{\\mathbb{R}^3}} {{u}^2}=c^2$, where $a\\!>\\!0$, $b\\!>\\!0$, $c\\!>\\!0$, $2\\!<\\!q\\!<\\!\\frac{14}{3}\\!<\\! p\\!\\leq\\!6$ or $\\frac{14}{3}\\!<\\!q\\!<\\! p\\!\\leq\\! 6$, $\\mu\\!>\\!0$ and $\\lambda\\!\\in\\!\\R$ appears as a Lagrange multiplier. In both cases for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.08106","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/2103.08106/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"}