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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. Functional Analysis 3 (1969), 217–245. MR 0244812
  • 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. 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
  • 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′skiĭ, Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0096983
    M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964. MR 0159197
  • 8. L. Kronecker, Ueber Systeme von Funktionen mehrerer Variabeln, Monatsber. Berlin Akad., 1869, 159-193; 688-698.
  • 9. Jean Leray, La théorie des points fixes et ses applications en analyse, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R. I., 1952, pp. 202–208 (French). MR 0047318
  • 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 vector spaces, J. Differential Equations 12 (1972), 610–636. MR 0328703
  • 12. Carlo Miranda, Problemi di esistenza in analisi funzionale, Quaderni Matematici, no. 3, Litografia Tacchi, Pisa, 1949 (Italian). Scuola Normale Superiore, Pisa. MR 0037461
  • 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, 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.

Review Information:

Reviewer: Jean Mawhin
Affiliation: Université Catholique de Louvain
Journal: Bull. Amer. Math. Soc. 34 (1997), 197-201
Review copyright: © Copyright 1997 American Mathematical Society