Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
W. V. Petryshyn
Title:
Generalized topological degree and semilinear equations
Additional book information:
Cambridge Tracts in Mathematics, vol. 117, Cambridge University Press,
Cambridge,
1995,
x+240 pp.,
ISBN 0-521-44474-8,
$59.95$
1. G.D. Birkhoff and O.D. Kellogg, Invariant points in function spaces, Trans. Amer. Math. Soc. 23 (1922) 96-115.
2. L.E.J. Brouwer, Ueber Abbildungen von Mannigfaltigkeiten, Math. Ann. 71 (1912), 97-115.
F. E. Browder and W. V. Petryshyn, Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Functional Analysis 3 (1969), 217–245. MR 0244812, DOI 10.1016/0022-1236(69)90041-x
4. R. Caccioppoli, Sulle corrispondenze funzionali inverse diramate: teoria generale a applicazioni ad alcune equizioni non lineari e al problema di Plateau. Rend. Accad. Lincei (6) 24 (1936) 258-263; 416-421.
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0
6. J. Hadamard, Sur quelques applications de l'indice de Kronecker, in J. Tannery, Introduction à la théorie des fonctions d'une variable, vol. 2, Hermann, Paris, 1910, 875-915.
M. A. Krasnosel′skiĭ, Topologicheskie metody v teoriĭ nelineĭnykh integral′nykh uravneniĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0096983
8. L. Kronecker, Ueber Systeme von Funktionen mehrerer Variabeln, Monatsber. Berlin Akad., 1869, 159-193; 688-698.
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
10. J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. (3) 51 (1934), 45-78.
J. Mawhin, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. Differential Equations 12 (1972), 610–636. MR 328703, DOI 10.1016/0022-0396(72)90028-9
Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
13. M. Nagumo, Degree of Mapping and Existence Theorems, Kawade, Tokyo, 1948 (in Japanese).
14. H. Poincaré, Sur les fonctions 
Bull. Soc. Math. France 11 (1882-83), 129-134.
15. H. Poincaré, Sur certaines solutions particulières du problème des trois corps, Bull. Astron. 1 (1884), 65-74.
N. Rouche and J. Mawhin, Ordinary differential equations, Surveys and Reference Works in Mathematics, vol. 5, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. Stability and periodic solutions; Translated from the French and with a preface by R. E. Gaines. MR 615082
17. J. Schauder, Der Fixpuntsatz in Funktionalraumen, Studia Math. 2 (1930), 171-180.
- 1.
- G.D. Birkhoff and O.D. Kellogg, Invariant points in function spaces, Trans. Amer. Math. Soc. 23 (1922) 96-115.
- 2.
- L.E.J. Brouwer, Ueber Abbildungen von Mannigfaltigkeiten, Math. Ann. 71 (1912), 97-115.
- 3.
- F.E. Browder and W.V. Petryshyn, Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Funct. Anal. 3 (1969), 217-245. MR 39:6126
- 4.
- R. Caccioppoli, Sulle corrispondenze funzionali inverse diramate: teoria generale a applicazioni ad alcune equizioni non lineari e al problema di Plateau. Rend. Accad. Lincei (6) 24 (1936) 258-263; 416-421.
- 5.
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of the Second Order, Springer, Berlin, 1983. MR 86c:35035
- 6.
- J. Hadamard, Sur quelques applications de l'indice de Kronecker, in J. Tannery, Introduction à la théorie des fonctions d'une variable, vol. 2, Hermann, Paris, 1910, 875-915.
- 7.
- M.A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostakhteoretizdat, Moscow, 1956. English transl. Pergamon, Oxford, 1964. MR 20:3464; MR 28:2414
- 8.
- L. Kronecker, Ueber Systeme von Funktionen mehrerer Variabeln, Monatsber. Berlin Akad., 1869, 159-193; 688-698.
- 9.
- J. Leray, La théorie des points fixes et ses applications en analyse, in Proc. Intern. Congress Mathematicians, Cambridge, Mass., 1950, Publ. Amer. Math. Soc., vol. 2, 1952, 202-208. MR 13:859a
- 10.
- J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. (3) 51 (1934), 45-78.
- 11.
- J. Mawhin, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological spaces, J. Differential Equations 12 (1972), 610-636. MR 48:7045
- 12.
- C. Miranda, Problemi di esistenza in analisi funzionale, Tacchi, Pisa, 1950. MR 12:265c
- 13.
- M. Nagumo, Degree of Mapping and Existence Theorems, Kawade, Tokyo, 1948 (in Japanese).
- 14.
- H. Poincaré, Sur les fonctions Bull. Soc. Math. France 11 (1882-83), 129-134.
- 15.
- H. Poincaré, Sur certaines solutions particulières du problème des trois corps, Bull. Astron. 1 (1884), 65-74.
- 16.
- N. Rouche and J. Mawhin, Ordinary Differential Equations, Pitman, Boston, 1980. MR 82i:34001
- 17.
- J. Schauder, Der Fixpuntsatz in Funktionalraumen, Studia Math. 2 (1930), 171-180.
Review Information:
Reviewer:
Jean Mawhin
Affiliation:
Université Catholique de Louvain
Email:
mawhin@amm.ucl.ac.be
Journal:
Bull. Amer. Math. Soc.
34 (1997), 197-201
DOI:
https://doi.org/10.1090/S0273-0979-97-00716-7
Review copyright:
© Copyright 1997
American Mathematical Society
