{"paper":{"title":"Ground states for a coupled nonlinear Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira","submitted_at":"2015-01-30T12:38:36Z","abstract_excerpt":"We study the existence of ground states for the coupled Schr\\\"odinger system\n  \\begin{equation} \\label{ellipticabstract} \\left\\{ \\begin{array}{llll} -\\Delta u+u&=&|u|^{2q-2}u+b|v|^q|u|^{q-2}u\\\\ -\\Delta v+\\omega^2v&=&|v|^{2q-2}v+b|u|^q|v|^{q-2}v \\end{array}\\right. \\end{equation} in $\\mathbf{R}^n$, for $\\omega \\geq 1$, $b>0$ (the so-called \"attractive case\") and $q>1$ ($q<\\frac n{n-2}$ if $n\\geq 3$). We improve for several ranges of $(q,n,\\omega)$ the known results concerning the existence of positive ground state solutions with non-trivial components. In particular, we prove that for $1<q<2$ su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07752","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"}