{"paper":{"title":"Global bifurcation techniques for Yamabe type equations on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alejandro Betancourt de la Parra, Jimmy Petean, Jurgen Julio-Batalla","submitted_at":"2019-05-22T18:04:55Z","abstract_excerpt":"We consider a closed Riemannian manifold $(M^n ,g)$ of dimension $n\\geq 3$ and study positive solutions of the equation $-\\Delta_g u + \\lambda u = \\lambda u^q$, with $\\lambda >0$, $q>1$. If $M$ supports a proper isoparametric function with focal varieties $M_1$, $M_2$ of dimension $d_1 \\geq d_2 $ we show that for any $q<\\frac{ n-d_2+2 }{n - d_2 -2}$ the number of positive solutions of the equation $-\\Delta_g u + \\lambda u = \\lambda u^q$ tends to $\\infty$ as $\\lambda \\rightarrow +\\infty$. We apply this result to prove multiplicity results for positive solutions of critical and supercritical equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09305","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"}