{"paper":{"title":"The energy identity of Sacks-Uhlenbeck operator and infinitely many solutions for Brezis-Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Fang","submitted_at":"2018-07-18T12:11:34Z","abstract_excerpt":"Let $\\Omega$ be a bounded smooth domain in $\\mathbb{R}^N$ with $N\\geq 3$, $1<\\alpha$, $2^{\\ast}=\\frac{2N}{N-2}$ and $\\{u_\\alpha\\}\\subset H_{0}^{1,2\\alpha}(\\Omega)$ be a critical point of the functional \\begin{equation*} I_{\\alpha,\\lambda}(u)=\\frac{1}{2\\alpha}\\int\\limits_{\\Omega} [(1+|\\nabla u|^2)^{\\alpha}-1 ]dx-\\frac{\\lambda}{2}\\int\\limits_{\\Omega}u^2dx-\\frac{1}{2^{\\ast}}\\int\\limits_{\\Omega}|u|^{2^{\\ast}}dx. \\end{equation*} In this paper, we obtain the limit behaviour of $u_\\alpha$ ( $\\alpha\\rightarrow 1$), energy identity, Pohozaev identity, some integral estimates, etc. And using these resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06886","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"}