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Nowak, Chr.; Stettner, H.

Nonuniqueness results for ordinary differential equations. (English) Zbl 0887.34003

Nonlinear Anal., Theory Methods Appl. 30, No. 6, 3935-3938 (1997).
Summary: We investigate the problem of nonuniqueness for the initial value problem \(\dot x=f(t,x)\), \(x(t_0)=x_0\), and analyze criteria for the existence of at least two different solutions. Some known conditions for nonuniqueness are revised.

Cited in 1 Document

MSC:

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

Keywords:

nonuniqueness; initial value problem
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\textit{Chr. Nowak} and \textit{H. Stettner}, Nonlinear Anal., Theory Methods Appl. 30, No. 6, 3935--3938 (1997; Zbl 0887.34003)
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References:

[1] Lakshmikantham, V., On the Kamke’s function in the uniqueness theorem of ordinary differential equations, (Proc. Nat. Acad. Sci. India Sect. A, 34 (1964)), 11-14 · Zbl 0166.34103
[2] Nowak, Chr., Eindeutigkeit und Nichteindeutigkeit bei gewöhnlichen Differentialgleichungen (1990), Habilitationsschrift: Habilitationsschrift Warszawa
[3] Nowak, Chr., Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations, Applicable Anal., 47, 39-44 (1992) · Zbl 0792.34002
[4] Nowak, Chr., Uniqueness and Nonuniqueness Results for Ordinary Differential Equations, (Bainov, D.; Dishliev, A., Plovdiv, Bulgaria, Aug.18-23,1994. Plovdiv, Bulgaria, Aug.18-23,1994, 5th International Colloquium on Differential Equations, Vol.2 (1995), SCT Publishing: SCT Publishing Klagenfurt), 140-147 · Zbl 0882.34003
[5] Stettner, H., Bemerkungen zur Nichteindeutigkeit bei gewöhnlichen Differentialgleichungen (1977), Klagenfurt, unpublished manuscript · Zbl 0297.34003
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