×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.