{"paper":{"title":"Mass Concentration and Local Uniqueness of Ground States for $L^2$-subcritical Nonlinear Schr\\\"{o}dinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shuai Li, Xincai Zhu","submitted_at":"2018-03-28T03:07:49Z","abstract_excerpt":"We consider ground states of $L^2$-subcritical nonlinear Schr\\\"{o}dinger equation (1.1), which can be described equivalently by minimizers of the following constraint minimization problem\n  $$ e(\\rho):=\\inf\\{E_{\\rho}(u):u\\in \\mathcal{H}(\\mathbb{R}^d),\\|u\\|_2^2=1\\}.$$ The energy functional $E_{\\rho}(u)$ is defined by $$ E_{\\rho}(u):=\\frac{1}{2}\\int_{\\mathbb{R}^d}|\\nabla u|^2dx +\\frac{1}{2}\\int_{\\mathbb{R}^d}V(x)|u|^2dx-\\frac{\\rho^{p-1}}{p+1}\\int_{\\mathbb{R}^d}|u|^{p+1}dx,$$ where $d\\geq1$, $\\rho>0$, $p\\in\\big(1, 1+\\frac{4}{d}\\big)$ and $0\\leq V(x)\\to\\infty$ as $|x| \\to\\infty$. We present a deta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10395","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"}