{"paper":{"title":"Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti","submitted_at":"2013-12-20T10:18:54Z","abstract_excerpt":"We study the asymptotic behavior, as $\\lambda \\rightarrow 0$, of least energy radial sign-changing solutions $u_\\lambda$, of the Brezis-Nirenberg problem\n  \\begin{equation*} \\begin{cases} -\\Delta u = \\lambda u + |u|^{2^* -2}u & \\hbox{in}\\ B_1\\\\ u=0 & \\hbox{on}\\ \\partial B_1, \\end{cases} \\end{equation*} where $\\lambda >0$, $2^*=\\frac{2n}{n-2}$ and $B_1$ is the unit ball of $\\R^n$, $n\\geq 7$.\n  We prove that both the positive and negative part $u_\\lambda^+$ and $u_\\lambda^-$ concentrate at the same point (which is the center) of the ball with different concentration speeds. Moreover we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5871","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"}