{"paper":{"title":"An optimal bound on the number of interior spike solutions for Lin-Ni-Takagi problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jing Zeng, Juncheng Wei, Weiwei Ao","submitted_at":"2012-09-13T09:13:45Z","abstract_excerpt":"We consider the following singularly perturbed Neumann problem {eqnarray*} \\ve^2 \\Delta u -u +u^p = 0 \\quad {{in}} \\quad \\Omega, \\quad u>0 \\quad {{in}} \\quad \\Omega, \\quad {\\partial u \\over \\partial \\nu}=0 \\quad {{on}} \\quad \\partial \\Omega, {eqnarray*} where $p$ is subcritical and $\\Omega$ is a smooth and bounded domain in $\\R^n$ with its unit outward normal $\\nu$. Lin-Ni-Wei \\cite{LNW} proved that there exists $\\ve_0$ such that for $0<\\ve<\\ve_0$ and for each integer $k$ bounded by {equation} 1\\leq k\\leq \\frac{\\delta(\\Omega,n,p)}{(\\ve |\\log \\ve |)^n} {equation} where $\\delta(\\Omega,n,p)$ is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2824","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"}