{"paper":{"title":"Multiple positive normalized solutions for nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Louis Jeanjean, Tianxiang Gou","submitted_at":"2017-05-26T15:16:14Z","abstract_excerpt":"We consider the existence of multiple positive solutions to the nonlinear Schr\\\"odinger systems sets on $H^1(\\mathbb{R}^N) \\times H^1(\\mathbb{R}^N)$, \\[ \\left\\{ \\begin{aligned} -\\Delta u_1 &= \\lambda_1 u_1 + \\mu_1 |u_1|^{p_1 -2}u_1 + \\beta r_1 |u_1|^{r_1-2} u_1|u_2|^{r_2}, -\\Delta u_2 &= \\lambda_2 u_2 + \\mu_2 |u_2|^{p_2 -2}u_2 + \\beta r_2 |u_1|^{r_1} |u_2|^{r_2 -2} u_2, \\end{aligned} \\right. \\] under the constraint \\[ \\int_{\\mathbb{R}^N}|u_1|^2 \\, dx = a_1,\\quad \\int_{\\mathbb{R}^N}|u_2|^2 \\, dx = a_2. \\] Here $a_1, a_2 >0$ are prescribed, $\\mu_1, \\mu_2, \\beta>0$, and the frequencies $\\lambda_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09612","kind":"arxiv","version":2},"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"}