{"paper":{"title":"Concentration-compactness principle for nonlocal scalar field equations with critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego Ferraz, Jo\\~ao Marcos do \\'O","submitted_at":"2016-09-21T11:23:57Z","abstract_excerpt":"The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space $\\mathcal{D}^{s,2} (\\mathbb{R}^N)$ for $0<s<\\min\\{1,N/2\\}.$ As an application we establish Palais-Smale compactness for the Lagrangian associated to the fractional scalar field equation $(-\\Delta)^{s} u = f(x,u)$ for $0<s<1.$ Moreover, using an analytic framework based on $\\mathcal{D}^{s,2}(\\mathbb{R}^N),$ we obtain the existence of ground state solutions for a wide class of nonlinearities in the critical growth range."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06501","kind":"arxiv","version":3},"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"}