{"paper":{"title":"Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Anna Maria Micheletti, Marco G. Ghimenti","submitted_at":"2010-12-27T21:47:27Z","abstract_excerpt":"Given (M, g0) we consider the problem -{\\epsilon}^2Delta_{g0+h}u + u = (u+)^{p-1} with ({\\epsilon}, h) \\in (0, {\\epsilon}0) \\times B{\\rho}. Here B{\\rho} is a ball centered at 0 with radius {\\rho} in the Banach space of all Ck symmetric covariant 2-tensors on M. Using the Poincar\\'e polynomial of M, we give an estimate on the number of nonconstant solutions with low energy for ({\\epsilon}, h) belonging to a residual subset of (0, {\\epsilon}0) \\times B{\\rho}, for ({\\epsilon}0, {\\rho}) small enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5672","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"}