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Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations. (English) Zbl 0792.34002
M. Samimi [Appl. Anal. 13, 291-296 (1982; Zbl 0464.34005)] gives nonuniqueness theorems for initial value problems \(x'=f(t,x)\), \(x(0)=x_ 0\), where \(f\) is not defined at \(t=0\). But the result for the scalar case only holds with the additional assumption that one solution exists. The applicability of the revised theorem is shown. The result for the \(n\)- dimensional case is generalized.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:
[1] Lakshmikantham V., Proc. Nat. Acad. Sci. India Sect. 34 pp 11– (1964)
[2] Lakshmikantham V., Differential and integral inequalities (1969) · Zbl 0177.12403
[3] Chr. Nowak, Ein Nichteindeutigkeitssatz für gewöhnliche Differentialgleichungen, to appear.
[4] DOI: 10.1080/00036818208839400 · Zbl 0464.34005
[5] Stettner H., Bemerkungen zur Nichteindeutigkeit bei gewöhnlichen Differentialgleichungen (1977)
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