{"paper":{"title":"Nonlinear elliptic equations with a singular perturbation on compact Lie groups and Homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Weiping Yan, Yong Li","submitted_at":"2012-05-17T04:33:29Z","abstract_excerpt":"This paper is devoted to the study of a class of singular perturbation elliptic type problems on compact Lie groups or homogeneous spaces $\\mathcal{M}$. By constructing a suitable Nash-Moser-type iteration scheme on compact Lie groups and homogeneous spaces, we overcome the clusters of \"small divisor\" problem, then the existence of solutions for nonlinear elliptic equations with a singular perturbation is established. Especially, if $\\mathcal{M}$ is the standard torus $\\textbf{T}^n$ or the spheres $\\textbf{S}^n$, our result shows that there is a local uniqueness of spatially periodic solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3848","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"}