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Summary:
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.
References:
[1] R. P. Agarwal, V. Lakshmikantham: Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations. World Scientific, 1993. MR 1336820
[2] J. Kalas: Nonuniqueness for the solutions of ordinary differential equations. Czechoslovak Math. Journal 29 (1979), 105–112. MR 0518144 | 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. MR 0218635 | Zbl 0166.34103
[4] V. Lakshmikantham, S. Leela: Differential and Integral Inequalities. Vol. I, Academic Press, New York, 1969.
[5] Chr. Nowak: Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations. Applicable Anal. 47 (1992), 39–44. DOI 10.1080/00036819208840130 | MR 1214647 | Zbl 0792.34002
[6] Chr. Nowak: Uniqueness and nonuniqueness results for ordinary differential equations. (manuscript). Zbl 0882.34003
[7] M. Samimi: Nonuniqueness criteria for ordinary differential equations. Applicable Anal. 13 (1982), 291–296. DOI 10.1080/00036818208839400 | MR 0670663 | Zbl 0464.34005
[8] H. Stettner: Nichteindeutigkeit bei gewöhnlichen Differentialgleichungen. Math. Nachrichten 64 (1974), 233–237. DOI 10.1002/mana.19740640113 | MR 0357933 | Zbl 0297.34003
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