{"paper":{"title":"Blow-up behavior of ground states for a nonlinear Schr\\\"{o}dinger system with attractive and repulsive interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Huan-Song Zhou, Xiaoyu Zeng, Yujin Guo","submitted_at":"2017-10-03T11:48:49Z","abstract_excerpt":"We consider a nonlinear Schr\\\"odinger system arising in a two-component Bose-Einstein condensate (BEC) with attractive intraspecies interactions and repulsive interspecies interactions in $\\mathbb{R}^2$. We get ground states of this system by solving a constrained minimization problem. For some kinds of trapping potentials, we prove that the minimization problem has a minimizer if and only if the attractive interaction strength $a_i (i=1,2)$ of each component of the BEC system is strictly less than a threshold $a^*$. %attractive intraspecies interactions satisfies $a_i< %a^*= \\|Q\\|_2^2,\\ i=1,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01096","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":""},"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"}