{"paper":{"title":"Ground state solutions for a fractional Schr\\\"odinger equation with critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovany M. Figueiredo, Vincenzo Ambrosio","submitted_at":"2016-11-10T13:30:33Z","abstract_excerpt":"In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation \\begin{align*} (-\\Delta)^{s} u+V(x)u= f(u) \\mbox{ in } \\mathbb{R}^{N}, \\end{align*} where $s\\in (0,1)$, $N> 2s$, $(-\\Delta)^{s}$ is the fractional Laplacian, $V: \\mathbb{R}^{N}\\rightarrow \\mathbb{R}$ is a bounded potential satisfying suitable assumptions, and $f\\in C^{1, \\beta}(\\mathbb{R}, \\mathbb{R})$ has critical growth. We first analyze the case $V$ constant, and then we develop a Jeanjean-Tanaka argument \\cite{JT} to deal with the non autonomous case. As far as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03296","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"}