{"paper":{"title":"Two Positive Normalized Solutions and Phase Separation for Coupled Schr\\\"odinger Equations on Bounded Domain with L2-Supercritical and Sobolev Critical or Subcritical Exponent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linjie Song, Wenming Zou","submitted_at":"2023-11-28T15:07:35Z","abstract_excerpt":"In this paper we study the existence of positive normalized solutions of the following coupled Schr\\\"{o}dinger system: \\begin{align} \\left\\{ \\begin{aligned} & -\\Delta u = \\lambda_u u + \\mu_1 u^3 + \\beta uv^2, \\quad x \\in \\Omega, \\\\ & -\\Delta v = \\lambda_v v + \\mu_2 v^3 + \\beta u^2 v, \\quad x \\in \\Omega, \\\\ & u > 0, v > 0 \\quad \\text{in } \\Omega, \\quad u = v = 0 \\quad \\text{on } \\partial\\Omega, \\end{aligned} \\right. \\nonumber \\end{align} with the $L^2$ constraint \\begin{align} \\int_{\\Omega}|u|^2dx = c_1, \\quad \\quad \\int_{\\Omega}|v|^2dx = c_2, \\nonumber \\end{align} where $\\mu_1, \\mu_2 > 0$, $\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16861","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/2311.16861/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"}