{"paper":{"title":"Existence of bound and ground states for fractional coupled systems in $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edcarlos Domingos da Silva, Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","submitted_at":"2018-03-14T13:44:29Z","abstract_excerpt":"In this work we consider the following class of nonlocal linearly coupled systems involving Schr\\\"{o}dinger equations with fractional laplacian $$ \\left\\{ \\begin{array}{lr} (-\\Delta)^{s_{1}} u+V_{1}(x)u=f_{1}(u)+\\lambda(x)v, & x\\in\\mathbb{R}^{N}, (-\\Delta)^{s_{2}} v+V_{2}(x)v=f_{2}(v)+\\lambda(x)u, & x\\in\\mathbb{R}^{N}, \\end{array} \\right. $$ where $(-\\Delta)^{s}$ denotes de fractional Laplacian, $s_{1},s_{2}\\in(0,1)$ and $N\\geq2$. The coupling function $\\lambda:\\mathbb{R}^{N} \\rightarrow \\mathbb{R}$ is related with the potentials by $|\\lambda(x)|\\leq \\delta\\sqrt{V_{1}(x)V_{2}(x)}$, for some $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05276","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"}