{"paper":{"title":"Normalized ground states for Kirchhoff equations in ${\\mathbb{R}}^{3}$ with a critical nonlinearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Penghui Zhang, Zhiqing Han","submitted_at":"2021-03-12T09:51:29Z","abstract_excerpt":"This paper is concerned with the existence of ground states for a class of Kirchhoff type equation with combined power nonlinearities \\begin{equation*} -\\left(a+b\\int_{\\mathbb{R}^{3}}|\\nabla u(x)|^{2}\\right) \\Delta u =\\lambda u+|u|^{p-2}u+u^{5}\\quad \\ \\text{for some} \\ \\lambda\\in\\mathbb{R},\\quad x\\in\\mathbb{R}^{3}, \\end{equation*} with prescribed $L^{2}$-norm mass \\begin{equation*}\n  \\int_{\\mathbb{R}^{3}}u^{2}=c^{2} \\end{equation*} in Sobolev critical case and proves that the equation has a couple of solutions $(u_{c},\\lambda_{c})\\in S(c)\\times \\mathbb{R}$ for any $c>0$, $a,b >0$ and $\\frac{14"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.07174","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/2103.07174/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"}