MorsePalais 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), 921927
MSC (2000):
Primary 58E05, 35J20
Published electronically:
October 11, 2006
MathSciNet review:
2262891
Fulltext PDF Free Access
Abstract 
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Abstract: Using elementary differential calculus we get a version of the MorsePalais 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 MathematicsInformatics, National University of Hochiminh City, Vietnam
Email:
dmduc@hcmc.netnam.vn
Tran Vinh Hung
Affiliation:
Department of MathematicsInformatics, National University of Hochiminh City, Vietnam
Email:
vhungt@hcm.fpt.vn
Nguyen Tien Khai
Affiliation:
Department of MathematicsInformatics, National University of Hochiminh City, Vietnam
Email:
Than_Phongnym@yahoo.com
DOI:
http://dx.doi.org/10.1090/S000299390608662X
PII:
S 00029939(06)08662X
Keywords:
MorsePalais 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.
