Nonuniqueness results for ordinary differential equations. (English) Zbl 0957.34004

Kalas, Josef

Czech. Math. J. 48, No. 2, 373-384 (1998).

The author presents several criteria assuring nonuniqueness of the initial value problem \(x'=f(t,x)\), \(x(0)=x_0\), His results generalize a.o. the results due to Chr. Nowak [Appl. Anal. 47, No. 1, 39-44 (1992; Zbl 0792.34002)], M. Samimi [Appl. Anal. 13, 291-296 (1982; Zbl 0464.34005)] and H. Stettner [Math. Nachr. 64, 233-237 (1974; Zbl 0297.34003)].

Reviewer: M.Tvrdý (Praha)

MSC:

34A12

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

Keywords:

uniqueness and nonuniqueness of solutions; singular Cauchy problem; Lyapunov functions

Citations:

Zbl 0792.34002; Zbl 0464.34005; Zbl 0297.34003

References:

[1]	R. P. Agarwal, V. Lakshmikantham: Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations. World Scientific, 1993. · Zbl 0785.34003
[2]	J. Kalas: Nonuniqueness for the solutions of ordinary differential equations. Czechoslovak Math. Journal 29 (1979), 105-112. · Zbl 0396.34006
[3]	V. Lakshmikantham: On the Kamke’s function in the uniqueness theorem of ordinary differential equations. Proc. Nat. Acad. Sci. India Ser. A 34 (1964), 11-14. · Zbl 0166.34103
[4]	V. Lakshmikantham, S. Leela: Differential and Integral Inequalities. Vol. I, Academic Press, New York, 1969. · Zbl 0177.12403
[5]	Chr. Nowak: Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations. Applicable Anal. 47 (1992), 39-44. · Zbl 0792.34002
[6]	Chr. Nowak: Uniqueness and nonuniqueness results for ordinary differential equations. · Zbl 0882.34003
[7]	M. Samimi: Nonuniqueness criteria for ordinary differential equations. Applicable Anal. 13 (1982), 291-296. · Zbl 0464.34005
[8]	H. Stettner: Nichteindeutigkeit bei gewöhnlichen Differentialgleichungen. Math. Nachrichten 64 (1974), 233-237. · Zbl 0297.34003