{"paper":{"title":"Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qihan He, Shuangjie Peng, Yan-fang Peng","submitted_at":"2017-05-25T09:20:31Z","abstract_excerpt":"In this paper, we study the following fractional nonlinear Schr\\\"odinger system $$ \\left\\{% \\begin{array}{ll} (-\\Delta)^s u +u=\\mu_1 |u|^{2p-2}u+\\beta |v|^p|u|^{p-2}u,~~x\\in \\R^N,\\vspace{2mm}\\\\ (-\\Delta)^s v +v=\\mu_2 |v|^{2p-2}v+\\beta |u|^p|v|^{p-2}v,~~x\\in \\R^N, \\end{array}% \\right. $$ where $0<s<1, \\mu_1 >0, \\mu_2>0, 1<p<2_s^*/2, 2_s^*=+\\infty$ for $N\\le 2s$ and $2_s^*=2N/(N-2s)$ for $N>2s$, and $\\beta \\in \\R$ is a coupling constant. We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $\\mu_1,\\mu_2, p, \\beta$. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09100","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"}