{"paper":{"title":"Positive radial solutions for coupled Schr\\\"{o}dinger system with critical exponent in $\\R^N\\,(N\\geq5)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong-yu Ye, Yan-fang Peng","submitted_at":"2013-08-14T13:23:33Z","abstract_excerpt":"We study the following coupled Schr\\\"odinger system \\ds -\\Delta u+u=u^{2^*-1}+\\be u^{\\frac{2^*}{2}-1}v^{\\frac{2^*}{2}}+\\la_1u^{\\al-1}, &x\\in \\R^N, \\ds -\\Delta v+v=v^{2^*-1}+\\be u^{\\frac{2^*}{2}}v^{\\frac{2^*}{2}-1}+\\la_2v^{r-1}, &x\\in \\R^N, u,v > 0, &x\\in \\R^N, where $N\\geq 5, \\la_1,\\la_2>0,\\be\\neq 0, 2<\\al,r<2^*,2^*\\triangleq \\frac{2N}{N-2}.$ Note that the nonlinearity and the coupling terms are both critical. Using the Mountain Pass Theorem, Ekeland's variational principle and Nehari mainfold, we show that this critical system has a positive radial solution for positive $\\be$ and some negativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3115","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"}