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Morse-Palais lemma for nonsmooth functionals on normed spaces |
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| Authors: | Duong Minh Duc Tran Vinh Hung Nguyen Tien Khai |
| Institution: | Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam ; Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam ; Department of Mathematics-Informatics, National University of Hochiminh City, Vietnam |
| 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. |
| Keywords: | Morse--Palais lemma normed spaces directional differentiability |
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