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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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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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: http://dx.doi.org/10.1090/S0002-9939-06-08662-X
PII: S 0002-9939(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.