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

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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[1] Lakshmikantham, V., On the Kamke’s function in the uniqueness theorem of ordinary differential equations, (), 11-14 · Zbl 0166.34103
[2] Nowak, Chr., Eindeutigkeit und nichteindeutigkeit bei gewöhnlichen differentialgleichungen, (1990), 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, (), 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[5] Stettner, H., Bemerkungen zur nichteindeutigkeit bei gewöhnlichen differentialgleichungen, (1977), Klagenfurt, unpublished manuscript · Zbl 0297.34003
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