Morse-Palais lemma for nonsmooth functionals on normed spaces

Authors:
Duong Minh Duc, Tran Vinh Hung and Nguyen Tien Khai

Journal:
Proc. Amer. Math. Soc. **135** (2007), 921-927

MSC (2000):
Primary 58E05, 35J20

Published electronically:
October 11, 2006

MathSciNet review:
2262891

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Abstract | References | Similar Articles | Additional Information

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 -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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Additional Information

**Duong Minh Duc**

Affiliation:
Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam

Email:
dmduc@hcmc.netnam.vn

**Tran Vinh Hung**

Affiliation:
Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam

Email:
vhungt@hcm.fpt.vn

**Nguyen Tien Khai**

Affiliation:
Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam

Email:
Than_Phongnym@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9939-06-08662-X

Keywords:
Morse--Palais lemma,
normed spaces,
directional differentiability

Received by editor(s):
October 6, 2005

Published electronically:
October 11, 2006

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.