{"paper":{"title":"Normalized solutions to Schr\\\"{o}dinger systems with potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhaoyang Yun","submitted_at":"2024-06-19T04:23:28Z","abstract_excerpt":"In this paper, we study the normalized solutions of the Schr\\\"{o}dinger system with trapping potentials \\begin{equation}\\label{eq:diricichlet} \\begin{cases} -\\Delta u_1+V_1(x)u_1-\\lambda_1 u_1=\\mu_1 u_1^3+\\beta u_1u_2^{2}+\\kappa u_2~\\hbox{in}~ \\mathbb{R}^3,\\\\ -\\Delta u_2+V_2(x)u_2-\\lambda_2 u_2=\\mu_2 u_2^3+\\beta u_1^2u_2+\\kappa u_1~\\hbox{in}~ \\mathbb{R}^3,\n  u_1\\in H^1(\\mathbb{R}^3), u_2\\in H^1(\\mathbb{R}^3),\\nonumber \\end{cases} \\end{equation} under the constraint \\begin{equation} \\int_{\\mathbb{R}^3} u_1^2=a_1^2,~\\int_{\\mathbb{R}^3} u_2^2=a_2^2\\nonumber, \\end{equation} where $\\mu_1,\\mu_2,a_1,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13204","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/2406.13204/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"}