{"paper":{"title":"Bifurcations for a Coupled Schr\\\"odinger System with Multiple Components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rushun Tian, Thomas Bartsch, Zhi-qiang Wang","submitted_at":"2014-08-20T11:43:43Z","abstract_excerpt":"In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: \\begin{equation*}\n  \\left\\{\\begin{array}{ll}\n  -\\Delta u_j + au_j = \\mu_ju_j^3+\\beta\\sum_{k\\ne j}u_k^2u_j,\n  u_j>0\\ \\ \\hbox{in}\\ \\Omega, u_j=0 \\ \\ \\hbox{on}\\ \\partial\\Omega,\\ j=1,\\dots,n.\n  \\end{array}\n  \\right. \\end{equation*} Here $\\Omega\\subset{\\mathbb{R}}^N$ is a smooth and bounded domain, $n\\ge3$, $a<-\\Lambda_1$ where $\\Lambda_1$ is the principal eigenvalue of $(-\\Delta, H_0^1(\\Omega))$; $\\mu_j$ and $\\beta$ are real constants. Using the positive and non-degenerate solution of the scalar e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4613","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"}