{"paper":{"title":"Fractional nonlinear Schr\\\"odinger equations with singular potential in $\\mathbf R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guoyuan Chen, Youquan Zheng","submitted_at":"2015-11-30T01:05:07Z","abstract_excerpt":"We are interested in nonlinear fractional Schr\\\"odinger equations with singular potential of form \\begin{equation*} (-\\Delta)^su=\\frac{\\lambda}{|x|^{\\alpha}}u+|u|^{p-1}u,\\quad \\mathbf R^n\\setminus\\{0\\}, \\end{equation*} where $s\\in (0,1)$, $\\alpha>0$, $p\\ge1$ and $\\lambda\\in \\mathbf R$. Via Caffarelli-Silvestre extension method, we obtain existence, nonexistence, regularity and symmetry properties of solutions to this equation for various $\\alpha$, $p$ and $\\lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09124","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"}