{"paper":{"title":"Normalized solutions for a system of coupled cubic Schr\\\"odinger equations on $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Louis Jeanjean, Nicola Soave, Thomas Bartsch","submitted_at":"2015-06-07T13:38:18Z","abstract_excerpt":"We consider the system of coupled elliptic equations \\[ \\begin{cases} -\\Delta u - \\lambda_1 u = \\mu_1 u^3+ \\beta u v^2 \\\\ -\\Delta v- \\lambda_2 v = \\mu_2 v^3 +\\beta u^2 v \\end{cases} \\text{in $\\mathbb{R}^3$}, \\] and study the existence of positive solutions satisfying the additional condition \\[ \\int_{\\mathbb{R}^3} u^2 = a_1^2 \\quad \\text{and} \\quad \\int_{\\mathbb{R}^3} v^2 = a_2^2. \\] Assuming that $a_1,a_2,\\mu_1,\\mu_2$ are positive fixed quantities, we prove existence results for different ranges of the coupling parameter $\\beta>0$. The extension to systems with an arbitrary number of componen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02262","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"}