{"paper":{"title":"Local uniqueness of $m$-bubbling sequences for the Gel'fand equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aleks Jevnikar, Daniele Bartolucci, Wen Yang, Youngae Lee","submitted_at":"2018-04-10T07:11:23Z","abstract_excerpt":"We consider the Gel'fand problem, $$ \\begin{cases} \\Delta w_{\\varepsilon}+\\varepsilon^2 h e^{w_{\\varepsilon}}=0\\quad&\\mbox{in}\\quad\\Omega, w_{\\varepsilon}=0\\quad&\\mbox{on}\\quad\\partial\\Omega, \\end{cases} $$ where $h$ is a nonnegative function in ${\\Omega\\subset\\mathbb{R}^2}$. Under suitable assumptions on $h$ and $\\Omega$, we prove the local uniqueness of $m-$bubbling solutions for any $\\varepsilon>0$ small enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03376","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"}