{"paper":{"title":"Ground state solutions for fractional scalar field equations under a general critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Gaetano Siciliano, Giovany M. Figueiredo","submitted_at":"2016-10-14T21:34:07Z","abstract_excerpt":"In this paper we study existence of ground state solution to the following problem $$ (- \\Delta)^{\\alpha}u = g(u) \\ \\ \\mbox{in} \\ \\ \\mathbb{R}^{N}, \\ \\ u \\in H^{\\alpha}(\\mathbb R^N) $$ where $(-\\Delta)^{\\alpha}$ is the fractional Laplacian, $\\alpha\\in (0,1)$. We treat both cases $N\\geq2$ and $N=1$ with $\\alpha=1/2$. The function $g$ is a general nonlinearity of Berestycki-Lions type which is allowed to have critical growth: polynomial in case $N\\geq2$, exponential if $N=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04649","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"}