{"paper":{"title":"Minimal energy solutions and infinitely many bifurcating branches for a class of saturated nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2015-03-31T09:18:09Z","abstract_excerpt":"We prove a conjecture which was recently formulated by Maia, Montefusco, Pellacci saying that minimal energy solutions of the saturated nonlinear Schr\\\"odinger system \\begin{align*}\n  - \\Delta u + \\lambda_1 u &= \\frac{\\alpha u(\\alpha u^2+\\beta v^2)}{1+s(\\alpha u^2+\\beta v^2)}\n  \\qquad\\text{in }\\mathbb{R}^n, \\newline\n  - \\Delta v + \\lambda_2 v &= \\frac{\\beta v(\\alpha u^2+\\beta v^2)}{1+s(\\alpha u^2+\\beta v^2)}\\qquad\\text{in\n  }\\mathbb{R}^n \\end{align*} are necessarily semitrivial whenever $\\alpha,\\beta,\\lambda_1,\\lambda_2>0$ and $0<s<\\max\\{\\frac{\\alpha}{\\lambda_1},\\frac{\\beta}{\\lambda_2}\\}$ exce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08974","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"}