Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1567158
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
N. G. Lloyd
Title:
Degree theory
Additional book information:
Cambridge Tracts in Math., vol. 73, Cambridge Univ. Press, Cambridge, Great Britain, 1978, x + 172 pp., $21.00.
Herbert Amann and Stanley A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39–54. MR 346601, DOI 10.1007/BF01178975
Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188
Jane Cronin, Analytic functional mappings, Ann. of Math. (2) 58 (1953), 175–181. MR 57464, DOI 10.2307/1969827
Jane Cronin, Fixed points and topological degree in nonlinear analysis, Mathematical Surveys, No. 11, American Mathematical Society, Providence, R.I., 1964. MR 0164101
Günther Eisenack and Christian Fenske, Fixpunkttheorie, Bibliographisches Institut, Mannheim, 1978 (German). MR 516947
6. L. Führer, Theorie des Abbildungsgrades in endlich-dimensionalen Räumen, Dissertation, Freie Univ., Berlin, 1971.
7. J. Hadamard, Sur quelques applications de l'indice de Kronecker, Introduction à la Théorie des Fonctions d'une Variable, vol. 2, by J. Tannery (Hermann, Paris, 1910).
Erhard Heinz, An elementary analytic theory of the degree of mapping in $n$-dimensional space, J. Math. Mech. 8 (1959), 231–247. MR 0102580, DOI 10.1512/iumj.1959.8.58017
C. A. S. Isnard, The topological degree on Banach manifolds, Global analysis and its applications (Lectures, Internat. Sem. Course, Internat. Centre Theoret. Phys., Trieste, 1972) Internat. Atomic Energy Agency, Vienna, 1974, pp. 291–313. MR 0436193
10. L. Kronecker, Über die Charakteristik von Functionen-Systemen, Monatsber, Kgl. Preuss, Akad. Wiss. 1878, 145-152.
Jean Leray and Jules Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45–78 (French). MR 1509338
N. G. Lloyd, On analytic differential equations, Proc. London Math. Soc. (3) 30 (1975), no. 4, 430–444. MR 385243, DOI 10.1112/plms/s3-30.4.430
Roger D. Nussbaum, On the uniqueness of the topological degree for $k$-set-contractions, Math. Z. 137 (1974), 1–6. MR 361951, DOI 10.1007/BF01213930
Roger D. Nussbaum, Generalizing the fixed point index, Math. Ann. 228 (1977), no. 3, 259–278. MR 440587, DOI 10.1007/BF01420294
Paul H. Rabinowitz, A note on topological degree theory for holomorphic maps, Israel J. Math. 16 (1973), 46–52. MR 346183, DOI 10.1007/BF02761969
J. Schwartz, Compact analytic mappings of $B$-spaces and a theorem of Jane Cronin, Comm. Pure Appl. Math. 16 (1963), 253–260. MR 163178, DOI 10.1002/cpa.3160160303
J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher. MR 0433481
J. R. L. Webb, Remarks on $k$-set contractions, Boll. Un. Mat. Ital. (4) 4 (1971), 614–629 (English, with Italian summary). MR 0293467
19. G. T. Whyburn, Topological analysis, Princeton Univ. Press, Princeton, N. J., 1958.
- 1.
- H. Amann and S. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39-54. MR 0346601
- 2.
- F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., vol. 18, part 2, Amer. Math. Soc. Providence, R. I., 1976. MR 405188
- 3.
- J. Cronin, Analytic functional mappings, Ann. of Math. (2) 58 (1953), 175-181. MR 57464
- 4.
- J. Cronin, Fixed points and topological degree in nonlinear analysis, Math. Surveys, no. 11, Amer. Math. Soc., Providence, R. I., 1964. MR 164101
- 5.
- G. Eisenack and C. Fenske, Fixpunkttheorie, Bibliographisches Institut, Zürich, 1978. MR 516947
- 6.
- L. Führer, Theorie des Abbildungsgrades in endlich-dimensionalen Räumen, Dissertation, Freie Univ., Berlin, 1971.
- 7.
- J. Hadamard, Sur quelques applications de l'indice de Kronecker, Introduction à la Théorie des Fonctions d'une Variable, vol. 2, by J. Tannery (Hermann, Paris, 1910).
- 8.
- E. Heinz, An elementary analytic theory of the degree of mappings in n-dimensional spaces, J. Math. Mech. Anal. 8 (1959), 231-247. MR 102580
- 9.
- C. Isnard, The topological degree on Banach manifolds, Global Analysis and its Applications, vol. II, pp. 291-313 (Vienna: International Atomic Energy Agency, 1974). MR 436193
- 10.
- L. Kronecker, Über die Charakteristik von Functionen-Systemen, Monatsber, Kgl. Preuss, Akad. Wiss. 1878, 145-152.
- 11.
- J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45-78. MR 1509338
- 12.
- N. G. Lloyd, On analytic differential equations, Proc. London Math. Soc. 30 (1975), 430-444. MR 385243
- 13.
- R. D. Nussbaum, On the uniqueness of the topological degree for k-set-contractions, Math. Z. 137 (1974), 1-6. MR 361951
- 14.
- R. D. Nussbaum, Generalizing the fixed point index, Math. Ann. 228 (1977), 259-278. MR 440587
- 15.
- P. H. Rabinowitz, A note on topological degree for holomorphic maps, Israel J. Math. 16 (1973), 46-52. MR 346183
- 16.
- J. T. Schwartz, Compact analytic mappings of B-spaces and a theorem of Jane Cronin, Comm. Pure Appl. Math. 16 (1963), 253-260. MR 163178
- 17.
- J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach, New York, 1969. MR 433481
- 18.
- J. R. L. Webb, Remarks on k-set-contractions, Boll. Un. Mat. Ital. 4 (1971), 614-629. MR 293467
- 19.
- G. T. Whyburn, Topological analysis, Princeton Univ. Press, Princeton, N. J., 1958.
Review Information:
Reviewer:
Roger D. Nussbaum
Journal:
Bull. Amer. Math. Soc.
1 (1979), 632-636
DOI:
https://doi.org/10.1090/S0273-0979-1979-14644-5
