{"paper":{"title":"Coupled elliptic systems involving the square root of the Laplacian and Trudinger-Moser critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","submitted_at":"2017-08-01T18:02:01Z","abstract_excerpt":"In this paper we prove the existence of a nonnegative ground state solution to the following class of coupled systems involving Schr\\\"{o}dinger equations with square root of the Laplacian\n  $$\n  \\left\\{\n  \\begin{array}{lr}\n  (-\\Delta)^{1/2}u+V_{1}(x)u=f_{1}(u)+\\lambda(x)v, & x\\in\\mathbb{R},\n  (-\\Delta)^{1/2}v+V_{2}(x)v=f_{2}(v)+\\lambda(x)u, & x\\in\\mathbb{R},\n  \\end{array}\n  \\right.\n  $$\n  where the nonlinearities $f_{1}(s)$ and $f_{2}(s)$ have exponential critical growth of the Trudinger-Moser type, the potentials $V_{1}(x)$ and $V_{2}(x)$ are nonnegative and periodic. Moreover, we assume that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00457","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"}