{"paper":{"title":"On Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bin Xu, Jun Yang, Suting Wei","submitted_at":"2016-03-23T13:25:57Z","abstract_excerpt":"We consider the problem $$\n  \\epsilon^2 \\Delta u-V(y)u+u^p\\,=\\,0,~~u>0~~\\quad\\mbox{in}\\quad\\Omega,~~\\quad\\frac {\\partial u}{\\partial \\nu}\\,=\\,0\\quad\\mbox{on}~~~\\partial \\Omega, $$ where $\\Omega$ is a bounded domain in $\\mathbb R^2$ with smooth boundary, the exponent $p>1$, $\\epsilon>0$ is a small parameter, $V$ is a uniformly positive, smooth potential on $\\bar{\\Omega}$, and $\\nu$ denotes the outward normal of $\\partial \\Omega$. Let $\\Gamma$ be a curve intersecting orthogonally with $\\partial \\Omega$ at exactly two points and dividing $\\Omega$ into two parts. Moreover, $\\Gamma$ satisfies stati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07175","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"}