The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinity

Abstract

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-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.

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

References in corpus (2)

• The splitting lemmas for nonsmooth functionals on Hilbert spaces I
• Some critical point theorems and applications