{"paper":{"title":"Uniqueness of bound states for sublinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengxiang Zhang, Xu Zhang","submitted_at":"2026-06-16T12:10:07Z","abstract_excerpt":"We investigate the uniqueness of radial bound state solutions to the sublinear elliptic equation \\[ \\begin{cases} -\\Delta u - u + |u|^{q-2}u = 0 & \\text{in } \\mathbb{R}^n, \\\\ u(x) \\to 0 & \\text{as } |x| \\to \\infty, \\end{cases} \\] where $q\\in(1,2)$ and $n\\geq 2$. We prove that for any prescribed integer $k\\geq 1$, the equation admits exactly one radial bound state solution with $k$ simple zeros. Furthermore, we consider the superlinear equation \\[ \\begin{cases} -\\Delta u + u -|u|^{p-1}u = 0 & \\text{in } \\mathbb{R}^n, \\\\ u(x) \\to 0 & \\text{as } |x| \\to \\infty. \\end{cases} \\] While the uniqueness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17840","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17840/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}