{"paper":{"title":"Minimal energy solutions for repulsive 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":"2013-03-19T09:21:59Z","abstract_excerpt":"In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schr\\\"odinger system\n  \\begin{align*}\n  \\begin{gathered}\n  -\\Delta u + \\, u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \\quad\\text{in}\\R^n,\n  -\\Delta v + \\omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v\\quad\\text{in}\\R^n.\n  \\end{gathered}\n  \\end{align*}\n  We consider the repulsive case $b<0$ and assume that the exponent $q$ satisfies $1<q<\\frac{n}{n-2}$ in case $n\\geq 3$ and $1<q<\\infty$ in case $n=1$ or $n=2$. For space dimensions $n\\geq 2$ and arbitrary $b<0$ we prove the exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4521","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"}