{"paper":{"title":"Normalized ground states for the fractional nonlinear Schr\\\"{o}dinger equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Binhua Feng, Jiajia Ren, Qingxuan Wang","submitted_at":"2019-07-08T07:31:00Z","abstract_excerpt":"In this paper, we study the existence and instability of standing waves with a prescribed $L^2$-norm for the fractional Schr\\\"{o}dinger equation \\begin{equation} i\\partial_{t}\\psi=(-\\Delta)^{s}\\psi-f(\\psi), \\qquad (0.1)\\end{equation} where $0<s<1$, $f(\\psi)=|\\psi|^{p}\\psi$ with $\\frac{4s}{N}<p<\\frac{4s}{N-2s}$ or $f(\\psi)=(|x|^{-\\gamma}\\ast|\\psi|^2)\\psi$ with $2s<\\gamma<\\min\\{N,4s\\}$. To this end, we look for normalized solutions of the associated stationary equation \\begin{equation} (-\\Delta)^s u+\\omega u-f(u)=0. \\qquad (0.2) \\end{equation} Firstly, by constructing a suitable submanifold of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03433","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"}