Book Review
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MathSciNet review:
1567112
Full text of review:
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This review is available free of charge.
Book Information:
Author:
Melvyn S. Berger
Title:
Nonlinearity and functional analysis
Additional book information:
Academic Press, New York, San Francisco, London, 1977, xix + 415 pp., $24.50.
George D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc. 18 (1917), no. 2, 199–300. MR 1501070, DOI 10.1090/S0002-9947-1917-1501070-3
G. D. Birkhoff and O. D. Kellogg, Invariant points in function space, Trans. Amer. Math. Soc. 23 (1922), no. 1, 96–115. MR 1501192, DOI 10.1090/S0002-9947-1922-1501192-9
3. S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations integralés, Fund. Math. 3 (1922), 133-181.
Jean Leray and Jules Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45–78 (French). MR 1509338
5. V. I. Lomonosov, Invariant subspaces for the family of operators which commute with a completely continuous operator, Functional Anal. Appl. 8 (1973), 213-214.
L. A. Ljusternik, The topology of the calculus of variations in the large, Translations of Mathematical Monographs, Vol. 16, American Mathematical Society, Providence, R.I., 1966. Translated from the Russian by J. M. Danskin. MR 0217817
Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
8. J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.
- 1.
- G. D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc. 18 (1917), 199-300. MR 1501070
- 2.
- G. D. Birkhoff and O. D. Kellogg, Invariant points in function space, Trans. Amer. Math. Soc. 23 (1922), 96-115. MR 1501192
- 3.
- S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations integralés, Fund. Math. 3 (1922), 133-181.
- 4.
- J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. 51 (1934), 45-78. MR 1509338
- 5.
- V. I. Lomonosov, Invariant subspaces for the family of operators which commute with a completely continuous operator, Functional Anal. Appl. 8 (1973), 213-214.
- 6.
- L. Lyusternik, The topology of the calculus of variations in the large, Transl. Math. Monographs, vol. 16, Amer. Math. Soc., Providence, R.I., 1966. MR 217817
- 7.
- M. Morse, The calculus of variations in the large, Amer. Math. Soc. Colloq. Publ., no. 18, Amer. Math. Soc., Providence, R.I., 1934. MR 1451874
- 8.
- J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.
Review Information:
Reviewer:
P. M. Fitzpatrick
Journal:
Bull. Amer. Math. Soc.
1 (1979), 210-217
DOI:
https://doi.org/10.1090/S0273-0979-1979-14557-9
