{"paper":{"title":"Spectral asymptotics of radial solutions and nonradial bifurcation for the H\\'enon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joel K\\\"ubler, Tobias Weth","submitted_at":"2019-01-02T17:32:31Z","abstract_excerpt":"We study the spectral asymptotics of nodal (i.e., sign-changing) solutions of the problem\n  \\begin{equation*} (H) \\qquad \\qquad \\left \\{\n  \\begin{aligned}\n  -\\Delta u &=|x|^\\alpha |u|^{p-2}u&&\\qquad \\text{in ${\\bf B}$,} \\\\\n  u&=0&&\\qquad \\text{on $\\partial {\\bf B}$,}\n  \\end{aligned}\n  \\right.\n  \\end{equation*}\n  in the unit ball ${\\bf B} \\subset \\mathbb{R}^N,N\\geq 3$, $p>2$ in the limit $\\alpha \\to +\\infty$. More precisely, for a given positive integer $K$, we derive asymptotic $C^1$-expansions for the negative eigenvalues of the linearization of the unique radial solution $u_\\alpha$ of $(H)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00453","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"}