{"paper":{"title":"Nonradial solutions for the H\\'enon equation close to the threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pablo Figueroa, S\\'ergio L. N. Neves","submitted_at":"2017-08-30T04:34:29Z","abstract_excerpt":"We consider the H\\'enon problem \\begin{equation*} \\left\\{ \\begin{array} - - \\Delta u = |x|^{\\alpha} u^{\\frac{N+2+2\\alpha}{N-2}-\\varepsilon} & \\ \\ \\text{in} \\ B_1, \\\\ u > 0 & \\ \\ \\text{in} \\ B_1, \\\\ u=0 & \\ \\ \\text{on} \\ \\partial B_1, \\end{array} \\right. \\end{equation*} where $B_1$ is the unit ball in ${\\mathbb R}^N$ and $N\\geqslant 3$. For $\\varepsilon > 0$ small enough, we use $\\alpha$ as a paramenter and prove the existence of a branch of nonradial solutions that bifurcates from the radial one when $\\alpha$ is close to an even positive integer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09112","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"}