{"paper":{"title":"Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jimmy Petean, Juan Carlos Fern\\'andez, Oscar Palmas","submitted_at":"2019-08-21T19:24:56Z","abstract_excerpt":"Given an isoparametric function $f$ on the $n$-dimensional round sphere, we consider functions of the form $u=w\\circ f$ to reduce the semilinear elliptic problem \\[ -\\Delta_{g_0}u+\\lambda u=\\lambda\\ | u\\ | ^{p-1}u\\qquad\\text{ on }\\mathbb{S}^n \\] with $\\lambda>0$ and $1<p$, into a singular ODE in $[0,\\pi]$ of the form $w'' + \\frac{h(r)}{\\sin r} w' + \\frac{\\lambda}{\\ell^2}\\ (| w|^{p-1}w - w\\ )=0$, where $h$ is an strictly decreasing function having exactly one zero in this interval and $\\ell$ is a geometric constant. Using a double shooting method, together with a result for oscillating solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08091","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08091/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}