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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On uniqueness theorems for ordinary differential equations and for partial differential equations of hyperbolic type


Authors: J. B. Diaz and W. L. Walter
Journal: Trans. Amer. Math. Soc. 96 (1960), 90-100
MSC: Primary 35.00; Secondary 34.00
MathSciNet review: 0120451
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  • [1] M. Nagumo, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Jap. J. Math. vol. 3 (1926) pp. 107-112.
  • [2] C. Carathéodory, Vorlesungen über reelle Funktionen, 2d ed., Berlin, 1927, pp. 665-674.
  • [3] E. Goursat, Cours d'analyse mathématique, 5 ed., vol. 1, 1927, pp. 42-43.
  • [4] Oskar Perron, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Math. Z. 28 (1928), no. 1, 216–219 (German). MR 1544953, http://dx.doi.org/10.1007/BF01181159
  • [5] E. Kamke, Differentialgleichungen reeller Funktionen, Leipzig, 1930, pp. 96-100.
  • [6] G. Sansone, Equazioni differenziali nel campo reale. II, Chapter 8, 2 ed., Bologna, 1949.
  • [7] Wolfgang Walter, Über die Differentialgleichung 𝑢_{𝑥𝑦}=𝑓(𝑥,𝑦,𝑢,𝑢ₓ,𝑢_{𝑦}), Math. Z. 71 (1959), 308–324 (German). MR 0132299 (24 #A2144)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1960-0120451-1
PII: S 0002-9947(1960)0120451-1
Article copyright: © Copyright 1960 American Mathematical Society