{"paper":{"title":"Ground states for a linearly coupled system of Schr\\\"odinger equations on $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","submitted_at":"2018-07-10T01:21:52Z","abstract_excerpt":"We study the following class of linearly coupled Schr\\\"{o}dinger elliptic systems $$\\left\\{  \\begin{array}{lr} -\\Delta u+V_{1}(x)u=\\mu|u|^{p-2}u+\\lambda(x)v, & \\quad x\\in\\mathbb{R}^{N}, \\\\ -\\Delta v+V_{2}(x)v=|v|^{q-2}v+\\lambda(x)u, & x\\in\\mathbb{R}^{N}, \\end{array} \\right. $$ where $N\\geq3$, $2<p\\leq q\\leq 2^{*}=2N/(N-2)$ and $\\mu\\geq0$. We consider nonnegative potentials periodic or asymptotically periodic which are related with the coupling term $\\lambda(x)$ by the assumption $|\\lambda(x)|\\leq\\delta\\sqrt{V_{1}(x)V_{2}(x)}$, for some $0<\\delta<1$. We deal with three cases: Firstly, we study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03436","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"}