{"paper":{"title":"Nonlinear Fractional Schr\\\"odinger Equations coupled by power-type nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Eduardo Colorado","submitted_at":"2021-11-09T16:07:24Z","abstract_excerpt":"In this work we study the following class of systems of coupled nonlinear fractional nonlinear Schr\\\"odinger equations, \\begin{equation*} \\left \\{ \\begin{array}{l} (-\\Delta)^s u_1+ \\lambda_1 u_1= \\mu_1 |u_1|^{2p-2}u_1+\\beta |u_2|^{p} |u_1|^{p-2}u_1 \\quad\\text{in }\\mathbb{R}^N,\\\\[3pt] (-\\Delta)^s u_2 + \\lambda_2 u_2= \\mu_2 |u_2|^{2p-2}u_2+\\beta |u_1|^{p}|u_2|^{p-2}u_2 \\quad\\text{in }\\mathbb{R}^N, \\end{array} \\right. \\end{equation*} where $ u_1,\\, u_2\\in W^{s,2}(\\mathbb{R}^N)$, with $ N=1,\\, 2,\\, 3$; $\\lambda_j,\\,\\mu_j>0$, $j=1,2$, $\\beta\\in \\mathbb{R}$, $p\\geq 2$ and $\\displaystyle\\frac{p-1}{2p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.05227","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.05227/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}