The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinity
Functional Analysis
2015-01-27 v2 Analysis of PDEs
Geometric Topology
Abstract
We generalize the Bartsch-Li's splitting lemma at infinity for -functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof is to combine the ideas of the Morse-Palais lemma due to Duc-Hung-Khai [9] with some techniques from [11], [17], [18]. A simple application is also presented.
Cite
@article{arxiv.1211.2128,
title = {The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinity},
author = {Guangcun Lu},
journal= {arXiv preprint arXiv:1211.2128},
year = {2015}
}
Comments
63 pages. Correcting Section 4 of the published version on [Topological Methods in Nonlinear Analysis, Vol.44, No.2, 2014] because there exist errors in the original one