Morse-palais lemma for nonsmooth functionals on normed spaces

Abstract

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the C1-smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple. © 2006 American Mathematical Society.