## 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

### Keywords:

nonuniqueness theorems; initial value problems

### Citations:

Zbl 0489.34001; Zbl 0464.34005
Full Text:

### 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)
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.