{"paper":{"title":"Uniqueness and nondegeneracy of sign-changing radial solutions to an almost critical elliptic problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Weiwei Ao, Wei Yao","submitted_at":"2015-10-15T19:37:04Z","abstract_excerpt":"We study sign-changing radial solutions for the following semi-linear elliptic equation \\begin{align*} \\Delta u-u+|u|^{p-1}u=0\\quad{\\rm{in}}\\ \\mathbb{R}^N,\\quad u\\in H^1(\\mathbb{R}^N), \\end{align*} where $1<p<\\frac{N+2}{N-2}$, $N\\geq3$. It is well-known that this equation has a unique positive radial solution and sign-changing radial solutions with exactly $k$ nodes. In this paper, we show that such sign-changing radial solution is also unique when $p$ is close to $\\frac{N+2}{N-2}$. Moreover, those solutions are non-degenerate, i.e., the kernel of the linearized operator is exactly $N$-dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04678","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"}