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Book Review

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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

References [Enhancements On Off] (What's this?)

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  • 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 $\Theta ,$ 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
MSC (1991): Primary 47H11, 34B15, 35J65
DOI: https://doi.org/10.1090/S0273-0979-97-00716-7
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society