{"paper":{"title":"Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domain: the $L^2$-supercritical case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linjie Song, Qiaoran Wu, Tianhao Liu, Wenming Zou","submitted_at":"2025-06-27T12:05:27Z","abstract_excerpt":"In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an $m$-coupled elliptic system of the Gross-Pitaevskii type:\n  \\begin{equation}\n  \\left\\{\n  \\begin{aligned}\n  &-\\Delta u_j + \\lambda_j u_j = \\sum_{k=1 }^m\\beta_{kj} u_k^2 u_j, \\quad u_j \\in H_0^1(\\Omega),\n  &\\int_\\Omega u_j^2dx = c_j, \\quad j = 1,2,\\cdots,m.\n  \\end{aligned}\n  \\right.\n  \\end{equation}\n  Here, $\\Omega \\subset \\mathbb{R}^N$ ($N = 3,4$) is a bounded domain. The constants $\\beta_{kj} \\neq 0$ and $c_j > 0$ are prescribed constants, while $\\lambda_1, \\cdots, \\lambda_m$ are unk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22152","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/2506.22152/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"}