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A generalization of the Nagumo uniqueness criterion. (English) Zbl 0389.34003


MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:

[1] Stephen R. Bernfeld, Rodney D. Driver, and V. Lakshmikantham, Uniqueness for ordinary differential equations, Math. Systems Theory 9 (1975/76), no. 4, 359 – 367. · Zbl 0329.34003 · doi:10.1007/BF01715361
[2] J. M. Bownds and F. T. Metcalf, An extension of the Nagumo uniqueness theorem, Proc. Amer. Math. Soc. 27 (1971), 313 – 316. · Zbl 0211.39604
[3] J. B. Diaz, On existence, uniqueness, and numerical evaluation of solutions of ordinary and hyperbolic differential equations, Ann. Mat. Pura Appl. (4) 52 (1960), 163 – 181. · Zbl 0100.29202 · doi:10.1007/BF02415674
[4] J. B. Diaz and W. L. Walter, On uniqueness theorems for ordinary differential equations and for partial differential equations of hyperbolic type, Trans. Amer. Math. Soc. 96 (1960), 90 – 100. · Zbl 0097.07001
[5] Einar Hille, Lectures on ordinary differential equations, Addison-Wesley Publ. Co., Reading, Mass.-London-Don Mills, Ont., 1969. · Zbl 0179.40301
[6] V. Lakshmikantham and S. Leela, Differential and integral inequalities, Vol. 1, Academic Press, New York, 1969. · Zbl 0177.12403
[7] M. Nagumo, Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Japan. J. Math. 3 (1926), 107-112. · JFM 52.0438.01
[8] Hirosi Okamura, Condition nécessaire et suffisante remplie par les équations différentielles ordinaires sans points de Peano, Mem. Coll. Sci. Kyoto Imp. Univ. Ser. A. 24 (1942), 21 – 28 (French). · Zbl 0061.17202
[9] Thomas Rogers, On Nagumo’s condition, Canad. Math. Bull. 15 (1972), 609 – 611. · Zbl 0254.34008 · doi:10.4153/CMB-1972-109-2
[10] Wolfgang Walter, Differential and integral inequalities, Translated from the German by Lisa Rosenblatt and Lawrence Shampine. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55, Springer-Verlag, New York-Berlin, 1970. · Zbl 0252.35005
[11] T. Yoshizawa, Stability theory by Liapunov’s second method, Math. Soc. Japan, Tokyo, 1966. · Zbl 0144.10802
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