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ISSN 1088-6826(e) ISSN 0002-9939(p)

Morse-Palais lemma for nonsmooth functionals on normed spaces

Author(s): Duong Minh Duc; Tran Vinh Hung; Nguyen Tien Khai
Journal: Proc. Amer. Math. Soc. 135 (2007), 921-927.
MSC (2000): Primary 58E05, 35J20
Posted: 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 $C^{1}$ -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

References:

1.: L.H. An, P.X. Du, D.M. Duc, and P.V. Tuoc, Lagrange multipliers for functions derivable along directions in a linear subspace, Proc. Amer. Math. Soc 133 (2005), 595-604. MR 2093084 (2005f:90152)
2.: K.C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhauser (1993). MR 1196690 (94e:58023)
3.: D.M. Duc, Nonlinear singular elliptic equations, London Math. Soc. 40 (1989), pp. 420-440. MR 1053612 (91g:35107)
4.: D.M. Duc and N.T. Vu, Nonuniformly elliptic equations of p-Laplacian type, Nonlinear Analysis, 61 (2005), pp. 1483-1495. MR 2135821 (2005k:35111)
5.: H. Hofer, The topological degree at a critical point of mountain-pass type, Proc. Sym. Pure. Math., 45 (1986), Part 1, pp. 501-509. MR 0843584 (87h:58031)
6.: N. Kuiper, $C^{1}$ -equivalence of functions near isolated critical points, Symposium on infinite dimensional Topology, Ann, Math. Studies 69 Princeton Univ. Press, Princeton (1972), pp. 199-218. MR 0413161 (54:1282)
7.: C. Li, S. Li, and J. Liu, Splitting theorem, Poincare-Hopf theorem and Jumping nonlinear problems, Functional Analysis, 221 (2005), pp. 439-455. MR 2124871
8.: J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, Appl. Math. Sci., Springer-Verlag 74 (1989). MR 0982267 (90e:58016)
9.: R.S. Palais, Morse theory on Hilbert manifolds, Topology, 2 (1963), pp. 299-340. MR 0158410 (28:1633)

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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: 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
Posted: October 11, 2006
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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