Morse–Palais lemma for nonsmooth functionals on normed spaces

Duc, Duong; Hung, Tran; Khai, Nguyen

doi:10.1090/S0002-9939-06-08662-X

Morse–Palais lemma for nonsmooth functionals on normed spaces
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by Duong Minh Duc, Tran Vinh Hung and Nguyen Tien Khai PDF

Proc. Amer. Math. Soc. 135 (2007), 921-927 Request permission

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 $C^{1}$-smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

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