{"paper":{"title":"High energy sign-changing solutions for Coron's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Monica Musso, Shengbing Deng","submitted_at":"2017-10-05T04:34:23Z","abstract_excerpt":"We study the existence of sign changing solutions to the following problem $$ (P) \\quad \\quad \\quad \\left\\{\n  \\begin{array}{ll} \\Delta u+|u|^{p-1}u=0 \\quad & {\\rm in} \\quad \\Omega_\\epsilon; u=0 \\quad & {\\rm on} \\quad\\partial \\Omega_\\epsilon,\n  \\end{array}\n  \\right. $$ where $p=\\frac{n+2}{n-2}$ is the critical Sobolev exponent and $\\Omega_\\epsilon$ is a bounded smooth domain in ${\\mathcal R}^n$, $n\\geq 3$, with the form $\\Omega_\\epsilon=\\Omega\\backslash B(0,\\epsilon)$ with $\\Omega$ a smooth bounded domain containing the origin $0$ and $B(0,\\epsilon)$ the ball centered at the origin with radius "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01880","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"}