{"paper":{"title":"Multiplicity and asymptotic profile of 2-nodal solutions to a semilinear elliptic problem on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Maria Micheletti, M\\'onica Clapp","submitted_at":"2013-01-01T22:58:31Z","abstract_excerpt":"We establish a lower bound for the number of sign changing solutions with precisely two nodal domains to the singularly perturbed nonlinear elliptic equation -{\\epsilon}^{2}{\\Delta}_{g}u+u=|u|^{p-2}u on an n-dimensional Riemannian manifold M, p in (2,2n/(n-2)), in terms of the cup-length of the configuration space of M. We give a precise description of the asymptotic profile of these solutions as {\\epsilon} goes to 0. We also provide new estimates for the cup-length of the configuration space of M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0143","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"}