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Lemme de Morse et calcul des variations. (French) Zbl 0414.58010


MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

[1] P. ANTOINE et F. VAN ISEGHEM : Conditions nécessaires et conditions suffisantes pour un minimum local d’une fonctionnelle . C.R.A.S. 282, pp. 523-526. MR 53 #9292 | Zbl 0329.49009 · Zbl 0329.49009
[2] P. ANTOINE : Conditions pour un minimum local d’une fonction différentiable . Pub. U.E.R. Math. Univ. Lille I n^\circ 97, 1976 .
[3] HUI-HSIUNG KUO : The Morse Palais lemma on Banach spaces . Bull. Amer. Soc. 80, 1974 , pp. 363-365. Article | MR 48 #12593 | Zbl 0277.58003 · Zbl 0277.58003 · doi:10.1090/S0002-9904-1974-13507-X
[4] M. MORSE : The calculus of variations in the large . Amer. Math. Soc. 1934 . · Zbl 0011.02802
[5] R. PALAIS : Morse theory on Hilbert manifolds . Topology 2, 1963 , pp. 299-340. MR 28 #1633 | Zbl 0122.10702 · Zbl 0122.10702 · doi:10.1016/0040-9383(63)90013-2
[6] R. PALAIS : The Morse lemma for Banach spaces . Bull. Amer. Math. Soc. 75, 1969 , pp. 968-971. Article | MR 40 #6593 | Zbl 0191.21704 · Zbl 0191.21704 · doi:10.1090/S0002-9904-1969-12318-9
[7] A.J.TROMBA : The Morse lemma on arbitrary Banach spaces . Bull. Amer. Math. Soc. 79, 1973 , pp. 85-86. Article | MR 46 #4567 | Zbl 0256.58004 · Zbl 0256.58004 · doi:10.1090/S0002-9904-1973-13104-0
[8] K. UHLENBECK : Morse theory on Banach manifolds . J. Funct. An. 10, 1972 , pp. 430-445. MR 51 #14148 | Zbl 0241.58002 · Zbl 0241.58002 · doi:10.1016/0022-1236(72)90039-0
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