{"paper":{"title":"Multiplicity of nodal solutions to the Yamabe problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan Carlos Fern\\'andez, M\\'onica Clapp","submitted_at":"2016-12-07T02:46:11Z","abstract_excerpt":"Given a compact Riemannian manifold $(M,g)$ without boundary of dimension $m\\geq 3$ and under some symmetry assumptions, we establish existence of one positive and multiple nodal solutions to the Yamabe-type equation $$-div_{g}(a\\nabla u)+bu=c|u|^{2^{\\ast}-2}u\\quad on\\ M$$ where $a,b,c\\in C^{\\infty}(M)$, $a$ and $c$ are positive, $-div_{g}(a\\nabla)+b$ is coercive, and $2^{\\ast}=\\frac{2m}{m-2}$ is the critical Sobolev exponent. In particular, if $R_{g}$ denotes the scalar curvature of $(M,g)$, we give conditions which guarantee that the Yamabe problem $$\\Delta_{g}u+\\frac{m-2}{4(m-1} R_{g}u=\\kap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02102","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"}