{"paper":{"title":"Positive normalized solutions to nonlinear elliptic systems in $\\R^4$ with critical Sobolev exponent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Xiaolong Yang, Xiao Luo","submitted_at":"2021-07-19T09:31:52Z","abstract_excerpt":"In this paper, we consider the existence and asymptotic behavior on mass of the positive solutions to the following system: \\begin{equation}\\label{eqA0.1}\\nonumber \\begin{cases} -\\Delta u+\\lambda_1u=\\mu_1u^3+\\alpha_1|u|^{p-2}u+\\beta v^2u\\quad&\\hbox{in}~\\R^4,\\\\ -\\Delta v+\\lambda_2v=\\mu_2v^3+\\alpha_2|v|^{p-2}v+\\beta u^2v\\quad&\\hbox{in}~\\R^4,\\\\ \\end{cases} \\end{equation} under the mass constraint $$\\int_{\\R^4}u^2=a_1^2\\quad\\text{and}\\quad\\int_{\\R^4}v^2=a_2^2,$$ where $a_1,a_2$ are prescribed, $\\mu_1,\\mu_2,\\beta>0$; $\\alpha_1,\\alpha_2\\in \\R$, $p\\!\\in\\! (2,4)$ and $\\lambda_1,\\lambda_2\\!\\in\\!\\R$ app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08708","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/2107.08708/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"}