{"paper":{"title":"Ground States for a nonlinear Schr\\\"odinger system with sublinear coupling terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira, Hugo Tavares","submitted_at":"2015-04-17T22:40:25Z","abstract_excerpt":"We study the existence of ground states for the coupled Schr\\\"odinger system\n  \\begin{equation} \\left\\{\\begin{array}{lll} \\displaystyle -\\Delta u_i+\\lambda_i u_i= \\mu_i |u_i|^{2q-2}u_i+\\sum_{j\\neq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i \\\\ u_i\\in H^1(\\mathbb{R}^n), \\quad i=1,\\ldots, d, \\end{array}\\right. \\end{equation} $n\\geq 1$, for $\\lambda_i,\\mu_i >0$, $b_{ij}=b_{ji}>0$ (the so-called \"symmetric attractive case\") and $1<q<n/(n-2)^+$. We prove the existence of a nonnegative ground state $(u_1^*,\\ldots,u_d^*)$ with $u_i^*$ radially decreasing. Moreover we show that, for $1<q<2$, such ground states are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04655","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"}