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.References
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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
- Received by editor(s): October 6, 2005
- Published electronically: October 11, 2006
- Communicated by: Jonathan M. Borwein
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 921-927
- MSC (2000): Primary 58E05, 35J20
- DOI: https://doi.org/10.1090/S0002-9939-06-08662-X
- MathSciNet review: 2262891