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

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

### Citations:

Zbl 0792.34002; Zbl 0464.34005; Zbl 0297.34003
Full Text:

### 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
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