{"paper":{"title":"The splitting lemmas for nonsmooth functionals on Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.FA","authors_text":"Guangcun Lu","submitted_at":"2011-02-10T09:28:28Z","abstract_excerpt":"The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for a class of continuously directional differentiable functionals (lower than $C^1$) on a Hilbert space $H$ which have higher smoothness (but lower than $C^2$) on a densely and continuously imbedded Banach space $X\\subset H$ near a critical point lying in $X$. (This splitting theorem generalize almost all previous ones to my knowledge). Moreover, a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2062","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"}