{"paper":{"title":"Ground state solution of fractional Schr\\\"odinger equations with a general nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi He","submitted_at":"2017-06-22T02:22:03Z","abstract_excerpt":"In this paper, we study the following fractional Schr\\\"odinger equation: \\[ \\left\\{\\begin{gathered}\n  {(- \\Delta)^s}u + mu = f(u){\\text{in}}{\\mathbb{R}^N}, \\hfill\n  u \\in {H^s}({\\mathbb{R}^N}),{\\text{}}u > 0{\\text{on}}{\\mathbb{R}^N}, \\hfill \\\\ \\end{gathered} \\right. \\] where $m>0$, $N>2s$, ${(- \\Delta)^s}$, $s \\in (0,1)$ is the fractional Laplacian. Using minimax arguments, we obtain a positive ground state solution under general conditions on $f$ which we believe to be almost optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07149","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"}